References

1. S. Abiteboul, K. Compton, and V. Vianu. Queries are easier than you thought (probably). In ACM Symp. on Principles of Database Systems, 1992, ACM Press, pages 23-32.

2. S. Abiteboul, L. Herr, and J. Van den Bussche. Temporal connectives versus explicit timestamps to query temporal databases. Journal of Computer and System Sciences, 58 (1999), 54-68.

3. S. Abiteboul, R. Hull, and V. Vianu. Foundations of Databases, Addison­Wesley, 1995.

4. S. Abiteboul, M. Y. Vardi, and V. Vianu. Fixpoint logics, relational machines, and computational complexity. Journal of the ACM, 44 (1997), 30-56.

5. S. Abiteboul and V. Vianu. Fixpoint extensions of first-order logic and datalog­like languages. In Proc. IEEE Symp. on Logic in Computer Science, 1989, pages 71-79.

6. S. Abiteboul and V. Vianu. Computing with first-order logic. Journal of Computer and System Sciences, 50 (1995), 309-335.

7. J.W. Addison, L. Henkin, A. Tarski, eds. The Theory of Models. North­Holland, 1965.

8. F. Afrati, S. Cosmadakis, and M. Yannakakis. On datalog vs. polynomial time. Journal of Computer and System Sciences, 51 (1995), 177-196.

9. A. Aho and J. Ullman. The universality of data retrieval languages. In Proc. ACM Symp. on Principles of Programming Languages, JgJg, ACM Press, pages 110-120.

10. M. Ajtai. Ef formulae on finite structures. Annals of Pure and Applied Logic, 24 (1983), 1-48.

11. M. Ajtai and R. Fagin. Reachability is harder for directed than for undirected graphs. Journal of Symbolic Logic, 55 (1990), 113-150.

12. M. Ajtai, R. Fagin, and L. Stockmeyer. The closure of monadic NP. Journal of Computer and System Sciences, 60 (2000), 660-716.

13. M. Ajtai andY. Gurevich. Monotone versus positive. Journal of the ACM, 34 (1987), 1004-1015.

292 References

14. G. Asser. Das Repriisentantenproblem im Pradikatenkalkiil der Ersten Stufe mit Identitat. Zeitschrift for Mathematische Logik und Grundlagen der Math­ematik, 1 (1955), 252--263.

15. D.A.M. Barrington, N. Immerman, C. Lautemann, N. Schweikardt, and D. Therien. The Crane Beach conjecture. In IEEE Symp. on Logic in Computer Science, 2001, pages 187--196.

16. D.A.M. Barrington, N. Immerman, and H. Straubing. On uniformity within NC1 . Journal of Computer and System Sciences, 41 (1990), 274-306.

17. J. Barwise. On Moschovakis closure ordinals. Journal of Symbolic Logic, 42 (1977), 292-296.

18. J. Barwise and S. Feferman, eds. Model- Theoretic Logics. Springer-Verlag, 1985.

19. M. Benedikt and L. Libkin. Relational queries over interpreted structures. Journal of the ACM, 47 (2000), 644-680.

20. M. Benedikt and L. Libkin. Tree extension algebras: logics, automata, and query languages. In IEEE Symp. on Logic in Computer Science, 2002, pagefi 203-212.

21. M. Benedikt, L. Libkin, T. Schwentick, and L. Segoufin. Definable relations and first-order query languages over strings. Journal of the ACM, 50 (2003), 694-751.

22. A. Blass, Y. Gurevich, and D. Kozen. A zero-one law for logic with a fixed-point operator. Information and Control, 67 (1985), 70- 90.

23. A. Blumensath and E. Gradel. Automatic structures. In IEEE Symp. on Logic in Computer Science, 2000, pages 51-62.

24. H. Bodlaender. A linear-time algorithm for finding tree-decompositions of small treewidth. SIAM Journal on Computing, 25 (1996), 1305-1317.

25. E. Borger, E. Gradel, and Y. Gurevich. The Classical Decision Problem. Springer-Verlag, 1997.

26. V. Bruyere, G. Hansel, C. Michaux, and R. Villemaire. Logic and p­recognizable sets of integers. Bulletin of the Belgian Mathematical Society, 1 (1994), 191-238.

27. J.R. Biichi. Weak second-order arithmetic and finite automata. Zeitschrift fiir Mathematische Logik und Grundlagen der Mathematik, 6 (1960), 66-92.

28. A. Bulatov. A dichotomy theorem for constraints on a three-dement set. IEEE Symp. on Foundations of Computer Science, 2002, pages 649-658.

29. S. R. Buss. First-order proof theory of arithmetic. In Handbook of Proof Theory, Elsevier, Amsterdam, 1998, pages 79-147.

30. J. Cai, M. Fiirer, and N. Immerman. On optimal lower bound on the number of variables for graph identification. Combinatorica, 12 (1992), 389-410.

31. P.J. Cameron. The random graph revisited. In Eur. Congr. of Mathematics, Vol. 1, Progress in Mathematics, Birkhauser, 2001, pages 267 274.

32. A. Chandra and D. Hare!. Computable queries for relational databases . .Jom·nal of Computer and System Sciences, 21 (1980), 156 178.

33. A. Chandra and D. Hare!. Structure and complexity of relational querief'. Journal of Computer and System Sciences, 25 (1982), 99-128.

References 293

34. A. Chandra and P. Merlin. Optimal implementation of conjunctive queries in relational data bases. In ACM Symp. on Theory of Computing, 1977, pages 77-90.

35. C.C. Chang and H.J. Keisler. Model Theory. North-Holland, 1990.

36. 0. Chapuis and P. Koiran. Definability of geometric properties in algebraically closed fields. Mathematical Logic Quarterly, 45 (1999), 533-550.

37. E. Clarke, 0. Grumberg, and D. Peled. Model Checking. The MIT Press, 1999.

38. H. Comon, M. Dauchet, R. Gilleron, F. Jacquemard, D. Lugiez, S. Tison, and M. Tommasi. Tree Automata: Techniques and Applications. Available at www.grappa.univ-lille3.fr/tata. October 2002.

39. S.A. Cook. The complexity of theorem-proving procedures. In Proc. ACM Symp. on Theory of Computing, 1971, ACM Press, pages 151-158.

40. S.A. Cook. Proof complexity and bounded arithmetic. Manuscript, Univ. of Toronto, 2002.

41. S.A. Cook andY. Liu. A complete axiomatization for blocks world. In Proc. 'lth Int. Symp. on Artificial Intelligence and Mathematics, January, 2002.

42. S. Cosmadakis. Logical reducibility and monadic NP. In Proc. IEEE Symp. on Foundations of Computer Science, 1993, pages 52-61.

43. S. Cosmadakis, H. Gaifman, P. Kanellakis, and M. Vardi. Decidable opti­mization problems for database logic programs. In ACM Symp. on Theory of Computing, 1988, pages 477-490.

44. B. Courcelle. Graph rewriting: an algebraic and logic approach. In Handbook of Theoretical Computer Science, Vol. B, North-Holland, 1990, pages 193--242.

45. B. Courcelle. On the expression of graph properties in some fragments of monadic second-order logic. In (134], pages 33-62.

46. B. Courcelle. The monadic second-order logic on graphs VI: on several repre­sentations of graphs by relational structures. Discrete Applied Mathematics, 54 (1994), 117-149.

47. B. Courcelle and J. Makowsky. Fusion in relational structures and the verifica­tion of monadic second-order properties. Mathematical Structures in Compute7' Science, 12 (2002), 203--235.

48. V. Dalmau, Ph. Kolaitis, and M. Vardi. Constraint satisfaction, bounded treewidth, and finite-variable logics. Proc. Principles and Practice of Con­straint Programming, Springer-Verlag LNCS 2470, 2002, pages 310-326.

49. A. Dawar. A restricted second order logic for finite structures. Logic and Computational Complexity, Springer-Verlag, LNCS 960, 1994, pages 393-413.

50. A. Dawar, K. Doets, S. Lindell, and S. Weinstein. Elementary properties of finite ranks. Mathematical Logic Quarterly, 44 (1998), 349-353.

51. A. Dawar andY. Gurevich. Fixed point logics. Bulletin of Symbolic Logic, 8 (2002), 65-88.

52. A. Dawar and L. Hella. The expressive power of finitely many generalized quantifiers. Information and Computation, 123 (1995), 172-184.

53. A. Dawar, S. Lindell, and S. Weinstein. Infinitary logic and inductive definabil­ity over finite structures. Information and Computation, 119 (1995), 160--175.

294 References

54. A. Dawar, S. Lindell, and S. Weinstein. First order logic, fixed point logic, and linear order. In Computer Science Logic, Springer-Verlag LNCS Vol. 1092, 1995, pages 161-177.

55. L. Denenberg, Y. Gurevich, and S. Shelah. Definability by constant-depth polynomial-size circuits. Information and Control, 70 (1986), 216-240.

56. M. de Rougemont. Second-order and inductive definability on finite struc­tures. Zeitschrift fur Mathematische Logik und Grundlagen der· Mathematik, 33 (1987), 47-63.

57. G. Dong, L. Libkin, and L. Wong. Local properties of query languages. Theo­retical Computer Science, 239 (2000), 277-308.

58. R. Downey and M. Fellows. Parameterized Complexity. Springer-Verlag, 1999.

59. D.-Z. Du, K.-1. Ko. Theory of Computational Complexity. Wiley-lnterscience, 2000.

60. H.-D. Ebbinghaus and J. Flum. Finite Model Theory. Springer-Verlag, 1995.

61. H.-D. Ebbinghaus, J. Flum, and W. Thomas. Mathematical Logic. Springer­Verlag, 1984.

62. A. Ehrenfeucht. An application of games to the completeness problem for formalized theories. Fundamenta Mathematicae, 49 (1961), 129-1,11.

63. T. Eiter, G. Gottlob, and Y. Gurevich. Existential second-order logic owr strings. Journal of the ACM, 47 (2000), 77-131.

64. E.A. Emerson. Temporal and modal logic. In Handbook of Theoretical Com-puter Science, Vol. B, North-Holland, 1990, pages 995-1072.

65. E.A. Emerson. Model checking and the mu-calculus. In [134], pages 185-214.

66. H. Enderton. A Mathematical Introduction to Logic. Academic-Press, 1972.

67. P. Erdos and A. Renyi. Asymmetric graphs. Acta Mathematicae Academiac Scientiarum Hungaricae, 14 (1963), 295 315.

68. K. Etessami. Counting quantifiers, successor relations, and logarithmic space. Journal of Computer and System Sciences, 54 (1997), 400-411.

69. K. Etessami, M.Y. Vardi, and T. Wilke. First-order logic with two variables and unary temporal logic. Information and Computation, 179 (2002), 279 -295.

70. R. Fagin. Generalized first-order spectra and polynomial-timP recognizable sets. In Complexity of Computation, R. Karp, ed., SIAM-AMS Proceedings, 7 (1974), 43-73.

71. R. Fagin. Monadic generalized spectra. Zeitschrift fiir Mathcmatische Logik und Grundlagen der Mathematik, 21 (1975), 89-96.

72. R. Fagin. A spectrum hierarchy. Zeitschrift fur Mathematische Logik und Grundlagen der Mathematik, 21 (1975), 123-134.

73. R. Fagin. Probabilities on finite models. Journal of Symbolic Logic, 41 (1976), 50--58.

74. R. Fagin. Finite-model theory-- a personal perspective. Theoretical Computer Science, 116 (1993), 3-31.

75. R. Fagin. Easier ways to win logical games. In [134], pages 1-32.

76. R. Fagin, L. Stockmeyer, and M.Y. Vardi. On monadic NP vs monadic co-NP. Information and Computation, 120 (1994), 78-92.

References 295

77. T. Feder and M.Y. Vardi. The computational structure of monotone monadic SNP and constraint satisfaction: a study through datalog and group theory. SIAM Journal on Computing, 28 (1998), 57-104.

78. T. Feder and M.Y. Vardi. Homomorphism closed vs. existential positive. IEEE Symp. on Logic in Computer Science, 2003, pages 311-320.

79. S. Feferman and R. Vaught. The first order properties of products of algebraic systems. Fundamenta Mathematicae, 47 (1959), 57-103.

80. J. Flum, M. Frick, and M. Grohe. Query evaluation via tree-decompositions. Journal of the ACM, 49 (2002), 716-752.

81. J. Flum and M. Grohe. Fixed-parameter tractability, definability, and model­checking. SIAM Journal on Computing 31 (2001), 113-145.

82. J. Flum and M. Ziegler. Pseudo-finite homogeneity and saturation. Journal of Symbolic Logic, 64 (1999), 1689-1699.

83. H. Fournier. Quantifier rank for parity of embedded finite models. Theoretical Computer Science, 295 (2003), 153-169.

84. R. Frai"sse. Sur quelques classifications des systemes de relations. Universite d'Alger, Publications Scientifiques, Serie A, 1 (1954), 35-182.

85. M. Frick and M. Grohe. The complexity of first-order and monadic second­order logic revisited. In IEEE Symp. on Logic in Computer Science, 2002, pages 215-224.

86. M. Furst, J. Saxe, and M. Sipser. Parity, circuits, and the polynomial-time hierarchy. Mathematical Systems Theory, 17 (1984), 13-27.

87. H. Gaifman. Concerning measures in first-order calculi. Israel Journal of Mathematics, 2 ( 1964), 1-17.

88. H. Gaifman. On local and non-local properties, Proc. Herbrand Symp., Logic Colloquium '81, North-Holland, 1982.

89. H. Gaifman and M.Y. Vardi. A simple proof that connectivity is not first-order definable. Bulletin of the EATCS, 26 (1985), 43-45.

90. F. Gecseg and M. Steinby. Tree languages. In Handbook of Formal Languages, Vol. 3. Springer-Verlag, 1997, pages 1-68.

91. F. Gire and H. K. Hoang. A more expressive deterministic query language with efficient symmetry-based choice construct. In Logic in Databases, Int. Work­shop LID'96, Springer-Verlag, 1996, pages 475-495.

92. Y.V. Glebskii, D.I. Kogan, M.A. Liogon'kii, and V.A. Talanov (IO. B. rJie6CKIIll, .n:. II. KoraH, M. II. JIIIorOHbKIIll, B. A. TaJiaHOB). Range and degree of realizability of formulas in predicate calculus ( 06beM II ,ll;Omr BhHIOJIHIIMOCTII <Pop My JI IIC'IIICJieHIIH rrpe,ll;IIKaTOB). Kibernetika (Ku6ep'ltemu1Ca), 2 (1969), 17-28.

93. G. Gottlob, E. Gradel, and H. Veith. Datalog LITE: a deductive query language with linear time model checking. ACM Transactions on Computational Logic, 3 (2002), 42-79.

94. G. Gottlob and C. Koch. Monadic datalog and the expressive power of lan­guages for Web information extraction. Journal of the ACM, 51 (2004), 74-113.

95. G. Gottlob, Ph. Kolaitis, and T. Schwentick. Existential second-order logic over graphs: charting the tractability frontier. In IEEE Symp. on Foundations

296 References

of Computer Science, 2000, pages 664-674.

96. G. Gottlob, N. Leone, and F. Scarcella. The complexity of acyclic conjunctive queries. Journal of the ACM, 48 (2001), 431-498.

97. E. Gradel. Capturing complexity classes by fragments of second order logic. Theoretical Computer Science, 101 (1992), 35-5 7.

98. E. Gradel andY. Gurevich. Metafinite model theory. Information and Com­putation, 140 (1998), 26-81.

99. E. Gradel, Ph. Kolaitis, L. Libkin, M. Marx, J. Spencer, M.Y. Vardi, Y. Ven­ema, S. Weinstein. Finite Model Theory and its Applications. Springer-Verlag, 2004.

100. E. Gradel, Ph. Kolaitis, and M.Y. Vardi. On the decision problem for two­variable first-order logic. Bulletin of Symbolic Logic, 3 (1997), 53 G9.

101. E. Gradel and G. McColm. On the power of deterministic transitive closures. Information and Computation, 119 (1995), 129-135.

102. E. Gradel and M. Otto. Inductive definability with counting on finite struc­tures. Proc. Computer Science Logic, 1992, Springer-Verlag, pages 231-24 7.

103. R.L. Graham, B.L. Rothschild and J.H. Spencer. Ramsey Theory. John Wiley & Sons, 1990.

104. E. Grandjean. Complexity of the first-order theory of almost all finite struc­tures. Information and Control, 57 (1983), 180-204.

105. E. Grandjean and F. Olive. Monadic logical definability of nondeterministic linear time. Computational Complexity, 7 (1998), 54-97.

106. M. Grohe. The structure of fixed-point logics. PhD Thesis, University of Freiburg, 1994.

107. M. Grohe. Fixed-point logics on planar graphs. In IEEE Symp. on Logic in Computer Science, 1998, pages 6-15.

108. M. Grohe. Equivalence in finite-variable logics is complete for polynomial time. Combinatorica, 19 (1999), 507--532.

109. M. Grohe. The parameterized complexity of database queries. In ACM Symp. on Principles of Database Systems, 2001, ACM Press, pages 82 -92.

110. M. Grohe. Large finite structures with few Lk-types. Information and Com­putation, 179 (2002), 250-278.

111. M. Grohe. Parameterized complexity for the database theorist. SIGMOD Record, 31 (2002), 86-96.

112. M. Grohe. The complexity of homomorphism and constraint satisfaction prob­lems seen from the other side. In IEEE Symp. on Foundations of Computer Science, 2003, pages 552-561.

113. M. Grohe and T. Schwentick. Locality of order-invariant first-order formulas. ACM Transactions on Computational Logic, 1 (2000), 112-130.

114. M. Grohe, T. Schwentick, and L. Segoufin. When is the evaluation of conjunc­tive queries tractable? In ACM Symp. on Theory of Computing, 2001, pages 657-666.

115. S. Grumbach and J. Su. Queries with arithmetical constraints. Theoretical Computer Science, 173 (1997), 151-181.

References 297

116. Y. Gurevich. Toward logic tailored for computational complexity. In Com­putation and Proof Theory, M. Richter et al., eds., Springer Lecture Notes in Mathematics, Vol. 1104, 1984, pages 175-216.

117. Y. Gurevich. Logic and the challenge of computer science. In Cnrrcnt trends in theoretical computer science, E. Borger, ed., Computer Science Press, 1988, pages 1 57.

118. Y. Gurevich, N. Immerman, and S. Shelah. McColm's conjecture. In IEEE Symp. on Logic in Computer Science, 1994, 10-19.

119. Y. Gurevich and S. Shelah. Fixed-point extensions of first-order logic. Annals of Pure and Applied Logic, 32 (1986), 265-280.

120. W. Hanf. Model-theoretic methods in the study of elementary logic. In [7], pages 132-145.

121. L. Rella. Logical hierarchies in PTIME. Information and Computation, 129 (1996), 1-19.

122. L. Rella, Ph. Kolaitis, and K. Luosto. Almost everywhere equivalence of logics in finite model theory. Bulletin of Symbolic Logic, 2 (1996), 422-443.

123. L. Rella, L. Libkin, and J. Nurmonen. Notions of locality and their logical characteri1:ations over finite models. Journal of Symbolic Logic, 64 (1999), 1751 1773.

124. L. Rella, L. Libkin, J. Nurmonen, and L. Wong. Logics with aggregate opera­tors. Journal of the ACM, 48 (2001), 880-907.

125. W. Hodges. Model Theory. Cambridge University Press, 1993. 126. J. Hopcroft and J. Ullman. Introduction to Automata Theory, Languages, and

Computation. Addison-Wesley, 1979.

127. R. Hull and J. Su. Domain independence and the relational calculus. Acta Informatica, 31 (1994), 513-524.

128. N. Immerman. Upper and lower bounds for first order expressibility. Journal of Computer and Sy8tem Sciences, 25 (1982), 76-98.

129. N. Immerman. Relational queries computable in polynomial time (extended abstract). In ACM Symp. on Theory of Computing, 1982, ACM Press, pages 147-152.

130. N. Immerman. Relational queries computable in polynomial time. Information and Control, 68 (1986), 86-104.

131. N. Immerman. Languages that capture complexity classes. SIAM Journal on Computing, 16 (1987), 760 778.

132. N. Immerman. Nondeterministic space is closed under complementation. SIAM Journal on Computing, 17 (1988), 935-938.

133. N. Immerman. Descriptive Complexity. Springer-Verlag, 1998. 134. N. Immerman and Ph. Kolaitis, eds. Descriptive Complexity and Finite Modds,

Proc. of a DIMACS workshop. AMS, 1997. 135. N. Immerman and E. Lander. Describing graphs: a first order approach

to graph canoni;r,ation. In Complexity Theory Retrospective, Springer-Verlag, Berlin, 1990.

136. N. Immerman and M.Y. Vardi. Model checking and transitive-closure logic. In Proc. Int. Conf. on Computer Aided Verification, Springer-Verlag LNCS 1254,

298 References

1997, pages 291-302.

137. D. Janin and J. Marcinkowski. A toolkit for first order extensions of monadic games. Proc. of Symp. on Theoretical Aspects of Computer Science, Springer­Verlag LNCS vol. 2010, Springer Verlag, 2001, 353-364.

138. D. Janin and I. Walukiewicz. On the expressive completeness of the propo­sitional mu-calculus with respect to monadic second order logic. In Proc. of CONCUR'96, Springer-Verlag LNCS 1119, 1996, pages 263-277.

139. D.S. Johnson. A catalog of complexity classes. In Handbook of Theoretical Computer Science, Vol. A, North-Holland, 1990, pages 67-161.

140. N. Jones and A. Selman. Thring machines and the spectra of first-order for­mulas. Journal of Symbolic Logic, 39 (1974), 139-150.

141. H. Kamp. Tense logic and the theory of linear order. PhD Thesis, University of California, Los Angeles, 1968.

142. P. Kanellakis, G. Kuper, and P. Revesz. Constraint query languages. Journal of Computer and System Sciences, 51 (1995), 26-52.

143. C. Karp. Finite quantifier equivalence. In [7], pages 407-412.

144. M. Kaufmann and S. Shelah. On random models of finite power and monadic logic. Discrete Mathematics, 54 (1985), 285-293.

145. B. Khoussainov and A. Nerode. Automata Theory and its Applications. Birkhiiuser, 2001.

146. S. Kleene. Arithmetical predicates and function quantifiers. Tran.~actions of the American Mathematical Society, 79 (1955), 312-340.

147. Ph. Kolaitis. Languages for polynomial-time queries - an ongoing quest. In Proc. 5th Int. Conf. on Database Theory, Springer-Verlag, 1995, pages 38 39.

148. Ph. Kolaitis. On the expressive power of logics on finite models. In [99].

149. Ph. Kolaitis and J. Viiiiniinen. Generalized quantifiers and pebble games on finite structures. Annals of Pure and Applied Logic, 74 (1995), 23-75.

150. Ph. Kolaitis and M.Y. Vardi. The decision problem for the probabilities of higher-order properties. In ACM Symp. on Theory of Computing, 1987, pages 425-435.

151. Ph. Kolaitis and M.Y. Vardi. 0-1 laws and decision problems for fragments of second-order logic. Information and Computation, 87 (1990), 301-337.

152. Ph. Kolaitis and M.Y. Vardi. Infinitary logic and 0-1 laws. Information and Computation, 98 (1992), 258-294.

153. Ph. Kolaitis and M.Y. Vardi. Fixpoint logic vs. infinitary logic in finite-model theory. In IEEE Symp. on Logic in Computer Science, 1992, pages 46 57.

154. Ph. Kolaitis and M.Y. Vardi. On the expressive power of Datalog: tools and a case study. Journal of Computer and System Sciences, 51 (1995), 110-134.

155. Ph. Kolaitis and M.Y. Vardi. 0-1 laws for fragments of existential second­order logic: a survey. In Proc. Mathematical Foundations of Computer Science, Springer-Verlag LNCS 1893, 2000, pages 84-98.

156. Ph. Kolaitis and M.Y. Vardi. Conjunctive-query containment and constraint satisfaction. Journal of Computer and System Sciences, 61 (2000), 302 332.

157. B. Kuijpers, J. Paredaens, and J. Van den Bussche. Topological elementary equivalence of closed semi-algebraic sets in the real plane . .Journal of Symbolic

References 299

Logic, 65 (2000), 1530-1555.

158. G. Kuper, L. Libkin, and J. Paredaens, eds. Constraint Databases. Springer­Verlag, 2000.

159. R.E. Ladner. On the structure of polynomial time reducibility. Journal of the ACM, 22 (1975), 155-171.

160. R.E. Ladner. Application of model theoretic games to discrete linear orders and finite automata. Information and Control, 33 (1977), 281-303.

161. C. Lautemann, N. Schweikardt, and T. Schwentick. A logical characterisation of linear time on nondeterministic Turing machines. In Proc. Symp. on Theoretical Aspects of Computer Science, Springer-Verlag LNCS 1563, 1999, pages 143-152.

162. C. Lautemann, T. Schwentick, and D. Therien. Logics for context-free lan­guages. In Proc. Computer Science Logic 1 gg4, Springer-Verlag, 1995, pages 205-216.

163. J.-M. Le Bars. Fragments of existential second-order logic without 0-1 laws. In IEEE Symp. on Logic in Computer Science, 1998, pages 525-536.

164. J.-M. LeBars. The 0-1 law fails for monadic existential second-order logic on undirected graphs. Information Processing Letters, 77 (2001), 43-48.

165. D. Leivant. Inductive definitions over finite structures. Information and Com­putation 89 (1990), 95 108.

166. L. Libkin. On counting logics and local properties. ACM Transactions on Computational Logic, 1 (2000), 33-59.

167. L. Libkin. Logics capturing local properties. ACM Transactions on Computa­tional Logic, 2 (2001), 135-153.

168. L. Libkin. Embedded finite models and constraint databases. In [99].

169. L. Libkin and L. Wong. Query languages for bags and aggregate functions. Journal of Computer and System Sciences, 55 (1997), 241-272.

170. L. Libkin and L. Wong. Lower bounds for invariant queries in logics with counting. Theoretical Computer Science, 288 (2002), 153-180.

171. S. Lindell. An analysis of fixed-point queries on binary trees. Thmretical Computer Science, 85 (1991), 75-95.

172. A.B. Livchak (A. B. JlnBLiaK). Languages for polynomial-time queries (5I3hiKH ,I\JUI rroJIHHOMHa.JihHhrx 3arrpocoB). In Computer-based Modeling and Optimiza­tion of Heat-power and Electrochemical Objects (Pac"lem u OnmuMuaau,uJ!, TenAomex1W"lec-x;ux u EAe-x;mpoxuMU"lec-x;ux 06lle-x;mo6 c Jlo.MOW,'b10 9BM), Sverdlovsk, 1982, page 41.

173. J. Lynch. Almost sure theories. Annals of Mathematical Logic, 18 (1980), 91-135.

174. J. Lynch. Complexity classes and theories of finite models. Mathematical Systems Theory, 15 (1982), 127-144.

175. R.C. Lyndon. An interpolation theorem in the predicate calculus. Pacific Journal of Mathematics, 9 (1959), 155-164.

176. J. Makowsky. Model theory and computer science: an appetizer. In Handbook of Logic in Computer Science, Vol. 1, Oxford University Press, 1992.

300 References

177. J. Makowsky. Algorithmic aspects of the Feferman-Vaught Theorem. Annals of Pure and Applied Logic, 126 (2004), 159-213.

178. J. Makowsky andY. Pnueli. Arity and alternation in second-order logic. Annals of Pure and Applied Logic, 78 (1996), 189-202.

179. J. Marcinkowski. Achilles, turtle, and undecidable boundedness problems for small datalog programs. SIAM Journal on Computing, 29 (1999), 231-257.

180. 0. Matz, N. Schweikardt, and W. Thomas. The monadic quantifier alternation hierarchy over grids and graphs. Information and Computation, 179 (2002), 356-383.

181. G.L. McColm. When is arithmetic possible? Annals of Pure and Applied Logic, 50 (1990), 29-51.

182. R. McNaughton and S. Papert. Counter-Free Automata. MIT Press, 1971.

183. F. Moller and A. Rabinovich. On the expressive power of CTL. In IEEE Symp. on Logic in Computer Science, 1999, pages 360-369.

184. M. Mortimer. On language with two variables. Zeitschrift fiir Mathematische Logik und Grundlagen der Mathematik, 21 (1975), 135-140.

185. Y. Moschovakis. Elementary Induction on Abstract Structures. North-Holland, 1974.

186. F. Neven. Automata theory for XML researchers. SIGMOD Record, 31 (2002), 39-46.

187. F. Neven and T. Schwentick. Query automata on finite trees. Theoretical Computer Science, 275 (2002), 633-674.

188. J. Nurmonen. On winning strategies with unary quantifiers. Jom·nal of Logir and Computation, 6 (1996), 779-798.

189. J. Nurmonen. Counting modulo quantifiers on finite structures. Information and Computation, 160 (2000), 62-87.

190. M. Otto. A note on the number of monadic quantifiers in monadic Ei. Infor­mation Processing Letters, 53 (1995), 337-339.

191. M. Otto. Bounded Variable Logics and Counting: A Study in Finite Models. Springer-Verlag, 1997.

192. M. Otto. Epsilon-logic is more expressive than first-order logic over finite structures. Journal of Symbolic Logic, 65 (2000), 1749--1757.

193. M. Otto and J. Van den Bussche. First-order queries on databaf'es embedded in an infinite structure. Information Processing Letters, 60 (1996), 37--41.

194. C. Papadimitriou. A note on the expressive power of Prolog. Bulletin of the EATCS, 26 (1985), 21--23.

195. C. Papadimitriou. Computational Complexity. Addison-Wesley, 1994.

196. C. Papadimitriou and M. Yannakakis. On the complexity of database queries. Journal of Computer and System Sciences, 58 (1999), 407 427.

197. J. Paredaens, J. Van den Bussche, and D. Van Gucht. First--order queries on finite structures over the reals. SIAM Journal on Computing, 27 (1998), 1747-1763.

198. A. Pillay and C. Steinhorn. Definable sets in ordered structures. III. Transac­tions of the American Mathematical Society, 309 (1988), 469--476.

References 301

199. E. Pezzoli. Computational complexity of Ehrenfeucht-Fra!sse games on finite structures. Computer Science Logic 1998, Springer-Verlag, LNCS 1584, pages 159 170.

200. B. Poizat. Deux ou trois choses que je sais de Ln. Journal of Symbolic Logic, 47 (1982), 641 658.

201. I3. Poizat. A Course in Model Theory: An Introduction to Contemporary Math­ematical Logic. Springer-Verlag, 2000.

202. M. Rabin. Decidability of second-order theories and automata on infinite trees. Transactions of the American Mathematical Society, 141 (1969), 1 35.

203. R. Rado. Universal graphs and universal functions. Acta Arithmetica, 9 (1964), 331 340.

204. N. Robertson and P. Seymour. Graph minors V. Excluding a planar graph. Journal of Combinatorial Theory, Series B, 41 (1986), 92-114.

205. N. Robertson and P. Seymour. Graph minors XIII. The disjoint paths problem. Journal of Combinatorial Theory, Series B, 63 (1995), 65-110.

206. J. Robinson. Definability and decision problems in arithmetic. Jour·nal of Symbolic Logic, 14 (1949), 98-114.

207. E. Rosen. Some aspects of model theory and finite structures. Bulletin of Symbolic Logic, 8 (2002), 380 403.

208. E. Rosen and S. 'Weinstein. Preservation theorems in finite model theory. In Logic and Computational Complexity, Springer-Verlag LNCS 960, 1994, pages 480 502.

209. J. Rosenstein. Linear Orderings. Academic Press, 1982.

210. B. Rossman. Successor-invariance in the finite. In IEEE Symp. on Logic in Computer Science, 2003, pages 148-157.

211. Y. Sagiv and M. Yannakakis. Equivalences among relational expressions with the union and difference operators. Journal of the ACM, 27 (1980), 633 655.

212. V. Sazonov. Polynomial computability and recursivity in finite domains. Elck­tronische Informationsverarbeitung und Kybernetik, 16 (1980), 319- 323.

213. T. Schaefer. The complexity of satisfiability problems. In Proc. 1Oth Symp. on Theory of Computing, 1978, pages 216-226.

214. K. Schneider. Verification of Reactive Systems. Springer-Verlag, 2004.

215. T. Schwentick. On winning Ehrenfencht games and monadic NP. Annals of Pure and Applied Logic, 79 (1996), 61-92.

216. T. Schwentick. Descriptive complexity, lower hounds and linear tim<'. In Proc. of Computer Science Logic, Springer-Verlag LNCS 1584, 1998, pages 9-28.

217. T. Schwentick and K. I3arthelmann. Local normal forms for first-order logic with applications to games and automata. In Proc. 15th Symp. on Theoretical Aspects of Computer Science {STAGS '98 ), Springer-Verlag, 1998, pages 444-454.

218. D. Seese. The structure of models of decidable monadic theories of graphs. Annals of Pure and Applied Logic, 53 (1991), 169-195.

219. D. Seese. Linear time computable problems and first-order descriptions. Math­ematical Structures in Computer Science, 6 (1996), 505 526.

302 Refermccs

220. 0. Shmucli. Decidability and expref'siveness of logic queries. In ACM Symp. on Principles of Database Systems, 1987, ACM Press, pag<'S 237 -24!).

221. M. Sipser. Introduction to the Theory of Computation. PINS Publishing, 1997.

222. L. Stockmeyer. The complexity of decision problems in automata and logic. PhD Thesis, MIT, 1974.

223. L. Stoc:kmeyer. The polynomial-time hierarchy. Theoretical Comput1T Science, 3 (1977), 1-22.

224. L. Stockmeyer and A. Meyer. Cosmological lower bound on the circuit com­plexity of a small problem in logic. Journal of the ACM, 49 (2002), 753 784.

225. H. Straubing. Finite Automata, Formal Logic, and Circuit Complr1:ity. Birkhauser, 1994.

226. R. S:zelepc:senyi. The method of forced enumeration for nondeterministic au­tomata. Acta Informatica, 26 (1988), 279 284.

227. V.A. Talanov and V.V. Knya:zev (B. A. Ta.;Janon, B.B. Kmnen). The asymptotic truth value of infinite formulas (06 aCIIl\IIITOTWH'CKmT :ma•Iemm IICTIIHHOCTH 6ec:KOHe'IHhiX <l>opMy.ri). Proc. All- Union seminar on discrete mathematics and its applir:ations (Mamepua.llibt Bcecmo:mozo Cc.,w,mwpa no Jl,uc'K:permwil MameMamU'K:C 7t ee IJpuAO:JICC'HU.ft.M), 1\Ioscow State University, Faculty of Mathematics and Mechanics, 1986, pages 56 61.

228. R. Tarjan and M. Yannakakis. Simple linear-time algorithms to test dwrdalit.v of graphs, test acyclicity of hypergraphs, and selectively reduce acyclic hypPr­graphs. SIAM Journal on Computing, 13 (1984), 566 -579.

229. A. Tarski. A Decision Method for Elementary Algebra and Geomdry. Univ. of California Press, 1951. Reprinted in Quantifier Elimination and Cylindrical Algebraic Decomposition, B. Caviness and J. Johnson, eds. Springer-Verlag, 1998, pages 24 84.

230. J. Thatcher and J. \\1right. Generali:zed finite automata theory with an ap­plication to a decision problem of second-order logic. Mathematical Systems Theory, 2 (1968), 57-81.

231. W. Thomas. Classifying regular events in symbolic logic. Journal of Computer and System Sciences, 25 (1982), 360 376.

232. W. Thomas. Logical aspects in the study of tree languages. In Pror. 9th Int. Colloq. on Trees in Algebra and Programming (CAAP'84), Cambridge University Press, 1984, pages 31 50.

233. \iV. Thomas. Languages, automata, and logic. In Handbook of Formal Lan­guage8, Vol. 3, Springer-Verlag, 1997, pages 389 455.

234. B. A. Trakhtenbrot (B.A. TpaxTeH6pOT). The impossibilty of an algorithm for the decision problem for finite models (H<'B03MO)f(IIOCTb a.'!ropHTl\Ia ll,.JIB

rrpo6JieMbi pa"3pemnMOCTII na KOHC'fHhiX K"'!accax). Doklady Amdernii Nank SSSR (Jl,o'K:AaBN A'K:aBeMuu Hay'K: CCCP), 70 (1950), 569-572.

235. E. Tsang. Foundations of Constraint Sati8faction. Academic PrPss, 1993.

236. G. Turan. On the definability of properties of finite graphs. Discn:tc Mathe­matics, 49 (1984), 291 -302.

237. J. Vaananen. Generalized quantifiers. Bulletin of the EATCS, 62 (1997), 1 Hi 136.

References 303

238 . .J. Vaananen. Unary quantifiers on finite models. Journal of Logic, Language

and Information, 6 (1997), 275 304.

239 . .J. Vaananen. A Short Course in Finite Model Theory. University of Helsinki. 44pp. Available at www .math. helsinki. fi/logic/people/ j ouko. vaananen.

240 . .J. van Benthem. Modal Logic and Classical Logic. Bibliopolis, 1983.

241. D. Van Dalen. Logic and Structure. Springer-Verlag, 1994.

242 . .J. Van den Bussche. Constraint databases: a tutorial introduction. SIGMOD

Record, 29 (2000), 44-51.

243. L. van den Dries. Tame Topology and 0-Minimal Structures. Cambridge Uni­versity Press, 1998.

244. M.Y. Vardi. The complexity of relational query languages. In Proc. ACM

Symp. on Theory of Computing, 1982, 137 146.

245. M.Y. Vardi. On the complexity of bounded-variable queries. In ACM Symp.

on Principles of Database Systems, ACM Press, 19~5, pages 266 -276.

246. M.Y. Vardi. Why is modal logic so robustly decidable? In [134], pages 149 183.

247. H. Vollmer. Introduction to Circuit Complexity. Springer-Verlag, 1999.

248. A . .J. Wilkie. Model completeness results for expansions of the ordered field of real numbers by restricted Pfaffian functions and the exponential function. Journal of the American Mathematical Society, 9 (1996), 1051-1094.

249. M. Yannakakis. Algorithms for acyclic database schemes. In Proc. Conf. on

Very Large Databases, 1981, pages 82-94.

250. M. Yannakakis. Perspectives on database theory. In IEEE Symp. on Founda­

tions of Computer Science, 1995, pages 224-246.

List of Notation

:J! 5

0" 13 2t 13 R 13 STRUCT[a] 14 FO 14 (2t, 2t') 15 O"n 16 ~ 17 'P(2t) 17 'P(2t, a) 17 E* 17 E 17 DTIME 19 NTIME 19 PTIME 19 NP 19 PSPACE 20 NLOG 20 DLoG 20 PH 20

Ef 20 !If 20

EVEN 24

=n 28 min 29 max 29 qr 32

FO[k] 32

tpk(2t, a) 34 ':':k 36 PARITY 41

B': 46 N,21 46 !::::; 47 hlr 47 lr 49 ;:::; 50 degree 55 deg_set 55 STRUCTt[a] 55 !::::;~~;;, 61

(FO + C);uv 69

(£+ <)inv 69

s': 74

enc(2t) 88

ll2t II 88 c 89 c 90 All 91 FO(+, x) 95 BIT 95 ~ 103 'H('P) 105 CQk 107

so 113 MSO 115 ::ISO 115 :JMSO 115 \ISO 115 \iMSO 115 MSO[k] 116

306 List of Notation

mso-tpk 116 tpFO' 220 _MSO 117 A<k 222

(:I') 222 FO(Cnt) 142 ::::;FO' 225 =-Ji:r 142 -<Fo' 226 FO(Q) 144 Ck 229 Loc'" 145 ([k 229 v 145 1\ 145 GRn 235 L:xcw(Cnt) 146 Jln(P) 235 #i'.;p 146 JI(P) 235 rk 146 E.An.n1 238 £::___"'(Cnt) 147 EAk 238 ~bl] 151 RQ 241 LagJ.!.r 159 EA 241

=JSO(r) 243 ~) 178 lfp 178 ad om 250 ifp 179 F0(9J1. 0') 250 pfp 180 =-J.rE ariom 250 }', 180 'i.r: E admn. 250 IFP 180 FOact (9J1. 0') 251 PFP 180 'Jl 253 LFP 181 RQC 255 LFP'tmutt 185 FQgcn(9J1, 0') 2G6 I 'PI Qj 189 R 260 /r!/~ 189 R!in 267 =-JLFP 197 TRCL 199 .n 278 trcl 199 O;p 279 POSTRCL 200 D;p 279

LTL 280 FOk 212 X 280 £~w 212 u 280 £w

XJ'" 212 CTL 280 PG 215 E 280 dom 218 A 280 rng 218 CTL* 280 I:J 218 JL.r ·'P 283 J., 218 CSP 286

Index

Ackermann class 275 Active domain 250

formula 251 quantifier 251

Aggregate logic 159

expressiveness of operator 159

160

Almost everywhere equivalence 245 Arity hierarchy 176 Asymptotic probability 235

of connectivity 236 of EVEN and parity 237 of extension axioms 238

Automaton and MSO 124 deterministic 17 nondeterministic 17 tree (ranked) 130 tree (unranked) 133

Back-and-forth 36 k 218

Ball 46 Bernays-Schonfinkel class 275 BNDP (bounded number of degrees

property) 55 Boolean combination 15

Capturing complexity class 168 coNP 169 DLoG 208 NLOG 200, 208

NP 169 PH 173 PSPACE 194 PTIME 192,208

Circuit Boolean 89 family of 90

uniform 95 majority, or threshold 155

Class of structures MSO-inductive 140 of bounded treewidth 110, 135 of small degree 55

Collapse active-generic 256, 257 natural-active 255 restricted quantifier 255

and VC dimension 273 fails over integers for the real field

to MSO 265 Combined complexity

260 261

of conjunctive queries 104 of FO 99 of LFP 207 of MSO 139

Completeness fails over finite models 166 of games for FO 35 of games for MSO 117

Complexity combined 88 data 88

308 Index

expression 88 fixed-parameter linear 100 fixed-parameter tractable 100 parameterized 100

Complexity class AC0 91 capturing of 168 coNP 20 DLoG 20 NEXPTIME 21 NLIN 139 NLoG 20 NP 19 PH 20 PTIME 19 TC0 155

Composition method for FO 30-31, 42 for MSO 118, 140

Conjecture Crane Beach 273 Gurevich's 204 McColm's 210, 234

Conjunctive query (CQ) 102 acyclic 105 combined complexity of 104 containment of 111 evaluation of 106, 107, 110, 111 union of 277

Connective Boolean 15 infinitary 145

Connectivity 23 and .C:::C,w(Cnt) 153 and embedded finite models 254,

260,265 and FO 23,37 and Hanf-locality 48 and MSO 120 topological 268, 272

Constraint satisfaction 285-288 and bounded treewidth 288 and conjunctive queries 286 and homomorphism 286 dichotomy for 287

Data complexity of FO 92 of FO(Cnt) 155

of LFP 194 of MSO 134

over strings and trees 135 of p.-calculus 284 of temporal logics 281 of TRCL 200-203

Database constraint 267 270 relational 1-4

DATALOG 196 and existential least fixed point logic

197 and PTIME 199 monotonicity of 197 with negation 196

Duplicator 26

Encoding of formulae 87 of structures 88

Extension axioms 238 and random graph 241 and zero-one law 240, 244 asymptotic probability of 238 using in collapse results 265

Extensional predicates 196

Failure in the finite Beth's theorem 42 compactness theorem 24 completeness theorem 166 Craig's theorem 42 Lowenheim-Skolem theorem 166 Los-Tarski theorem 42

Finite variable logic (.C~"') and fixed point logics 214 and pebble games 216 definition of 212

First-order logic (FO) 14 expressive power of 28-31, 37 40 games for 32

Fixed-parameter linearity of acyclic conjunctive queries 106 of FO for small degrees 101 of MSO and bounded trecwidth 135 of MSO over strings and trees 135 of temporal logics 281

Fixed-parameter tractability and bounded treewidth 110

of FO on planar graphs 102 Fixed point 178

inflationary 179 least 178 partial 180 simultaneous 184 stages of 184, 186, 188

FO with counting (FO(Cnt)) 142 Formula

atomic 14 C-invariant 68 Hintikka 40 quantifier-free 14

FPL 100 FPT 100

Gaifman graph 45 Gaifman-locality 48 Game

Ajtai-Fagin 123 and :3MSO 123

bijective 59, 151 and .C~w(Cnt) 151

Ehrenfeucht-Fralsse 26 for FO 26 for MSO 116

Fagin 122 pebble 215

and .C~w 216

Halting problem 19, 166 Hanf-locality 47 Hypergraph 105

tree decomposition of 105-108

Inexpressibility of connectivity

in FO(AII) 94 in :3MSO 120 in .C~w(Cnt) 153 of arbitrary graphs in FO 23 of finite graphs in FO 37, 52 using Hanf-locality 48

EVEN

in fixed point logics 217 inFO 25 in L~w 217 in MSO 118 of ordered sets 28

Hamil tonicity in MSO 126

Index 309

PARITY in FO(AII) 94 Inflationary fixed point logic (IFP)

180 Intensional predicates 196 Isomorphism 17

partial 27 with the k-back-and-forth property

218

Join 102

Kripke structure 278 bisimilarity of 284

Language 17 regular 18

and MSO 124 star-free 127

and FO 127 Least fixed point logic (LFP) 181 Linear order

affects expressive power 69, 119, 150,153,214

definability of 227 FO definability of 28-31

Locality of aggregate logic 160 of FO 52 of .C~w(Cnt) 153 of order-invariant FO 73

Locality rank 49 bounds on 54, 64 Hanf 47

Logic aggregate 159 CTL 280 CTL* 280 existential fixed point 197 finite variable 212 first-order 14 FO with counting 142 infinitary 145, 212 inflationary fixed point 180 least fixed point 181 L~w 212 L~w(Cnt) 147 LTL 280 monadic second-order 115

310 Index

JI-calculus 283 partial fixed point propositional modal sPcond-order 113

180 279

115 115

existential (=JSO) universal ('v'SO)

SO-HoR:\' 208 SO-KROM 208 transitive closure 199

l\fodd 13 embedded finite 250 finite 13

Model-checking problem 87, 100, 281 Monadic second-order logic (MSO)

115 existential (=JMSO) 115

equals MSO over strings 126 universal ('v'MSO) 115

differmt from =JMSO 120 JI-calculus (CALC1,) 283

Neighborhood 46 Normal form

for LFP 192, 194 for SO 115 for TRCL 201

Occurrence negative 181 positiw~ 181

Operator 178 based on a formula inductive 178

180

Order invariancP 69 separation results for

fixed point logics 217 FO 69 FO(Cnt) 158 L~w 214 L~w(Cnt) 153 MSO 119

undecidability of 174 Ordered conjecture 210

Partial fixed point logic (PFP) 180 Polynomial hierarchy 20

and MSO 134 capturing of 173

Polynomial time 19 capturing of

in =JSO 208 over onkred structures 192 over unordered structurPs 204 205

Projecticm 103 Property

bisimulation-invariant 285 fiuite mo(kl 276

and satisfiahility 276-278 Ramsey 257

and collapse 259 Propositional modal logic (ML) 279

Quantifier active domain 251 counting 1-11 existential 14 generalized

and PTir-.n: 20-1 Hartig 14-1 Rescher 144 unary 144

prefix rank

173,175,243,275 32

second-order 114 universal 14 unrPstrictecl 251

Quantifier elimination and collapse results 25:-J for the random graph 2·±7 for the real field 261

Query 17 Boolean 17 complexity of 88 conjunctive 102 definable in a logic 17 Gaifman-local -18 Hanf-local 47 invariant 68 order-invariant 69 weakly local 73

L(~. see Recursively enumerahk Random graph 241

and quantifier elimination 24 7 collapsP over 265 representations of 248 theory of 242

Rank in L~w(Cnt) 146 quantifier 32

for unary quantifiers 144 inFO 32 in SO 115

Reachability 2, 122 and Gaifman-locality 49 for directed graphs in 3MSO 122 for undirected graphs in 3MSO 122

Recursive 19 Recursively enumerable 19 RQC (restricted quantifier collapse)

255

Satisfiability for Ackermann class 277 for Bernays-Schonfinkel class 276 for F02 278

Second-order logic (SO) 113 Selection 103 Sentence 15

atomic 33 finitely satisfiable 165 finitely valid 165 quantifier rank of 32 satisfiable 16 valid 16

Simultaneous fixed point 184 elimination of 186

Sphere 74 Spoiler 26 Structure 13

canonical for FOk Kripke 278 rigid 234 k-rigid 227

Symbol constant 13 function 13 relation 13

Term 14 counting 146

Theorem

229

Abiteboul-Vianu 230 Ajtai's 94 Beth's 42 Biichi's 124

compactness 16 completeness 16 Cook's 173 Courcelle's 135 Craig's 42

Index 311

Ehrenfeucht-Fralsse 32 Fagin's 169 Furst-Saxe-Sipser 94 Gaifman's 60 Grohe-Schwentick 73 Gurevich's 69 Gurevich-Shelah 191 Immerman-Szelepcsenyi 200 Immerman-Vardi 192 Lowenheim-Skolem 16 Los-Tarski 42 Lyndon's 43 Ramsey's 257 Stage comparison 189 Tarski-Knaster 179 Trakhtenbrot's 165

Theory 16 complete 242 consistent 16 decidable 242 w-categorical 242

Threshold equivalence 61 Transitive closure 3, 17

expressible in DATALOG 196 expressible in fixed point logics 182 inexpressible in aggregate logic 160 inexpressible in FO 52 violates locality 49

Transitive closure logic (TRCL) 199 positive 200

Tree 129 automata 130 decomposition 105, 107 regular languages and MSO 131 unranked 132

automata 133 regular and MSO 133

Treewidth 107 bounded 108, 110, 135, 140

Turing machine 18 and logic 166-168, 170-172,

193-194, 201 deterministic 18 time and space bounds 19

312 Index

Type Variable atomic 226 FOk 220

Pxpressibility of 221 225 ordering of 227-229

in L:~w(Cnt) 152 rank-k, FO 34

cxpressibility of 35 finite number of 35

rank-k, MSO 116 and automata expressibility of

125 126 116

bound 15 free 14

Vocabulary 13 purely relational 14 relational 14

Zero-one law 2:37 and extension axioms 240 failure for 1\180 24 7 for c:;__w 237 for FO and fixed point logics 237 for fragments of SO 243 245

Name Index

Abiteboul, S. VIII, 206, 207, 229, 230, 232,246,288

Afrati, F. 207 Aho, A. VII Ajtai, M. 94, 108, 123, 136, 174, 206 Asser, G. 174

Barrington, D. A. M. 108, 161, 271 Barthelmann, K. 63 Barwise, .J. 232 Benedikt, M. 137, 270 Blass, A. 246, 247 Blumensath, A. 137 Bodlaender, H. 137 Borger, E. 288 Bruyere, V. 137 Biichi, .J. VIII, 11, 124, 136 Bulatov, A. 289 Buss, S. 108

Cai, .J. 206 Cameron, .J. Chandra, A. Chang, C.C.

246 VII, 108, 109, 206 21

Chapuis, 0. 271 Clarke, E. 288 Compton, K. 246 Cook, S. A. 40, 108, 174 Cosmadakis, S. 137, 207 Courcelle, B. 135, 137

Dalmau, V. 289 Dawar, A. 109, 206, 207, 232, 233 Denenberg, L. 108

de Rougemont, M. 136, 233 Dong, G. 63 Downey, R. 108

Ebbinghaus, H.-D. VIII, 21, 40, 83, 136, 206

Ehrenfeucht, A. 26, 32, 40 Eiter, T. 174 Emerson, E. A. 288 Enderton, H. 21 Erdos, P. 246 Etessami, K. 161, 288

Fagin, R. VII, 6, 62, 120, 122, 123, 136, 165,168-174, 193-195,200,204, 246

Feder, T. 40, 289 Feferman, S. 137, 232 Fellows, M. 108 Flum, .J. VIII, 21, 40, 83, 108-110, 136,

206,271 271

26,32,40 108, 109, 137 206

Fournier, H. Frai"sse, R. Frick, M. Fiirer, M. Furst, M. 94, 108

40,45,48,63,246

246

Gaifman, H. Gire, F. 206 Glebskii, Y. Gottlob, G. Gradel, E. Graham, R. Grandjean, E.

108,109,174,207,288 137,161,174,206,288

270 137, 246

314 Name Index

Grohc, M. 73, 83, 108-110, 137, 206, 207, 233, 289

Grumbach, S. 270 Grumberg, 0. 288 Gurevich, Yu. 40, 69, 73, 83, 108, 161,

174,191,192,204,206,228,246, 247,288

Hanf, IN. 47, 62 Hard, D. VII, 206 Rella, L. 63, 161, 206, 207, 246 Herr, L. 288 Hoang, H. 206 Hodges, W. 21, 246 Hopcroft, J. 11, 21 Hull, R. VIII, 206, 271

Immerman, N. VII, 108, 109, 161, 192, 195,200,206,226,232,271,288

Janin, D. 136, 289 Johnson, D. 21 .Jones, N. 174

Kamp, H. 288 Kanellakis, P. 136, 270 Karp, C. 246 Kaufmann, M. 246 Keisler, H. J. 21 Khoussainov, B. 21 Kleene, S. 174 Knaster, B. 179 Knyazev, V. 246 Koch, C. 207 Koiran, P. 271 Kolaitis, Ph. 161, 174, 206, 210, 232,

233,246,247,288,289 Ko7,en, D. 246, 247 Kuijpers, B. 271 Kuper, G. 270

Ladner, R. 136, 289 Lander, E. 161 Lautemann, C. 174,271 Le Bars, .J.-l\!1. 246, 247 Leivant, D. 206 Leone, N. 108, 109 Libkin, L. 63,83, 137,161,270 Lindell, S. 207,232,233

Livchak, A. B. 206 Luosto, K. 246 Lynch, J. 137, 246 Lyndon, R. 43, 207

Makowsky, .J. 40, 136, 137, 174 Marcinkowski, .J. 136, 207 Matz, 0. 137 McColm, G. 206, 210, 233 McNaughton, R. 136 MPrlin, P. 108, 109 Meyer, A. 137 Moller, F. 289 !'viortimer, l\L 288 Moschovakis, Y. 206

Nerode, A. 21 Neven, F. 136, 137 Nurmonen, J. 63. 161

Olive, F. 137 Otto, l\!1. 83, 137, 206, 207, 232, 270

Papadimitriou, C. 21, 108, 1()!), 206 PaperL S. 136 Paredaens, J. 270, 271 Pekd, D. 288

40 272

Pezzoli. E. Pillay, A. Pnndi, Y. Poizat, B.

174 21,232

Rabin, l\!1. 140 Rabinovich, A. 289 Rado, R. 246 Renyi, A. 246 Reves7,, P. 270 Robertson, N. 110, 140 Robinson, J. 271 Rosen, E. 40 Rosenstein, .J. 40 Rossman, B. 83 Rothschild, B. 270

Sagiv, Y. 288 Saxe, J. 94, 108 Sazonov, V. 206 Scarcello, F. 108, 109 Schaefer, T. 289 Schweikardt, N. 137, 271

Schwentick, T. 63, 73, 83, 108, 109, 136,137,174

Seese, D. 108, 137 Segoufin, L. 108, 109 Selman, A. 17 4 Seymour, P. 110, 140 Shelah, S. 108, 191, 192, 206, 207, 228,

246 Shmueli, 0. 207 Sipser, M. 21, 94, 108 Spencer, J. 270 Steinhorn, C. 272 Stockmeyer, L. 62,108,136,137,174 Straubing, H. 108, 161 Su, J. 270 Szelepcsenyi, R. 200, 206

Talanov, V. 246 Tarjan, R. 108 Tarski, A. 179, 271 Thatcher, J. 137 Therien, D. 174, 271 Thomas, W. VIII, 21, 136, 137 Trakhtenbrot, B. VII, 165, 166, 170,

171,174,193,195 Tunin, G. 136

Name Index 315

Ullman, J. D. VII, 11, 21

Vaiinanen, J. VIII, 161 van Benthem, J. 288 van Dalen, D. 21 Van den Bussche, J. 270, 271, 288 Van Gucht, D. 270 Vardi, M. Y. VII, 40, 62, 108, 136, 192,

195,200,206,210,226,232,233, 246,247,288,289

Vaught, R. 137 Veith, H. 288 Vianu, V. VIII, 206, 207, 229, 230, 232,

246 Vollmer, H. 109, 161

Walukiewicz, I. 289 Weinstein, S. 40, 207, 232, 233 Wilke, T. 288 Wilkie, A. 272 Wong, L. 63, 83 Wright, J. 137

Yannakakis, M. 108, 109, 206, 207, 288

Ziegler, M. 271

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S. Ronchi Della Rocca, L. Paolini The Parametric Lambda Calculus A Metamodel for Computation

Y. Bertot, P. Casteran Interactive Theorem Proving and Program Development Coq' Art: The Calculus of Inductive Constructions

L. Libkin Elements of Finite Model Theory