carlos damásiotapd 2000, vigo1 a distributed tabling system carlos viegas damásio...

Carlos Damásio TAPD 2000, Vigo 1

A Distributed Tabling System

Carlos Viegas Damásio ([email protected])

Dept. Informática, Univ. Nova de Lisboa

Portugal


Overview

• Objectives of this work

• The Distributed Tabling Architecture

• Architecture Components

• A running example

• Completion and Termination

• Conclusions


Objectives

• Define a general and “open” architecture for distributed tabled query-evaluation of definite logic programs.

• Address the issue of table completion resorting to known distributed algorithms.


Architecture Components

• 1 Goal Manager

• 1 Table Manager

• N Table Storage Clients

• N Prover Clients


Goal Manager

• Interfaces the distributed tabling system with the “outside” world.

• It accepts queries and provides answers to the queries.

• Detects termination of the computation


Table Manager

• Decides the location of the tables among the several table storage clients, guaranteeing uniqueness of the tables.

• If all prover clients know where a goal should be tabled, then the Table Manager can be removed from the architecture


Table Storage Clients

• Keep the answers for given goal calls, avoiding redundant answers.

• They manage the delivery of solutions to the appropriate invoking goals


Prover Clients

• Perform the logical expansion operations on the set of active goals.


Message Protocol

Goal Manager Table Manager

query(Vars, Body, N)

answer(Lit,Gid)

call(Lit,Gid)

Table Storage Prover

call(Lit,Gid)call(Lit,Gid)

table(Lit,TS)

call(Lit,Tid)

answer(Lit,Gid)

answer(Lit,Tid)

call(Lit,Gid)

answer(Vars, N)


Message Complexity

• Goal call:– at least 1 message and at most 4 messages.– If the table manager is not involved, at least 1

message and at most 2 messages.

• Answer return:– 1 plus the number of consumers of the table.

So, at least 2 messages.


An Example

a(X) b(X), c(X).

a(1).

b(X) a(X).

b(0).

c(0).

?- b(X).



1. query([X], b(X), 5)

2. assert(q0(X) b(X) )

table[q0(_)] := ts1

3. call(q0(X), 0)

Prover 1

T. Storage 1

Prover 2

T. Storage 2



6. table(q0(_), ts1)

7. call(q0(X),0)

tabling[q0(_)] := t0

consumer[t0] := {(gm,0)}

8. call(q0(X1),t0)

[t0] 0: q0(X1) b(X1)

9. call(b(X1),0)

tabling[b(_)] := t0

consumer[t0] := {(p1,0)}

10. call(b(X2),t0)

[t0] 0: b(X3) a(X3)

[t0] b(0).


Prover 2T. Storage 2

tabling[b(_)] := t0

consumer[t0] := (p1,0)

11. call(a(X3),0)

[t0] 0: b(X3) a(X3)

[t0] b(0).

tabling[a(_)] := t1


12. call(a(X4),t1)

[t1] 1: a(X4) b(X4), c(X4).

[t1] a(1).

13. answer(b(0),t0)

solution[t0] := b(0)

14. call(b(X4),1)

15. answer(a(1),t1)

, (p2,1)

solution[t1] := a(1)

16. answer(b(0),1)

17. answer(a(1),0)

[t0] b(1).

[t1] 2: a(0) c(0).

18. answer(b(1),t0)

, b(1)

19. answer(b(1),1)

[t1] 3: a(1) c(1).


Goal Manager

Prover 1

T. Storage 1

T. Storage 2

tabling[b(_)] := t0



, (p2,1)

20. answer(b(0),0)

, b(1)

[t0] 0: q0(X1) b(X1)

[t0] q0(0).

21. answer(q0(0),t0)



solution[t0] := q0(0)

22. answer(q0(0),0)

23. answer(0,5)

24. answer(b(1),0)


[t0] q0(1).

, q0(1)

26. answer(q0(1),0)

27. answer(1,5)


T. Storage 2

T. Storage 1

Prover 1

Prover 2

29. call(c(0),t1)

tabling[c(0)] := t1


solution[t1] := c(0)33. answer(c(0),2)

28. call(c(0),2)

tabling[b(_)] := t0


tabling[a(_)] := t1


solution[t0] := b(0), b(1)

solution[t1] := a(1)

[t0] 0: q0(X1) b(X1)

[t0] q0(0).

[t0] q0(1).

tabling[c(1)] := t2


[t0] 0: b(X3) a(X3)

[t0] b(0).

[t1] 1: a(X4) b(X4), c(X4).

[t1] a(1).

[t0] b(1).

[t1] 2: a(0) c(0).

[t1] 3: a(1) c(1).

30. call(c(1),3)

[t1] c(0).

31. call( c(1), t2) 32. answer(c(0),t1)

[t1] a(0).

35. answer(a(0),0)

34. answer(a(0),t1)

, a(0)

[t0] b(0).

36. answer(b(0),t0)


Termination Detection

• The computation stops when activity ceases in the system (no messages and all processes are idle).

• A classical distributed termination detection algorithm suffices to detect global termination (it doubles in the worst case the number of messages)


Completion Detection

• Completion is important for– Reclaiming of space and global evaluation

structures.– Evaluation of default negation (not...)

• Algorithm for distributed completion of tables without goal dependency propagation


Credit Recovery AlgorithmAction Effect

Sendp {statep = active}send <M,Wp/2> to q; Wp = Wp/2

Receivep {A basic message has arrived}receive message <M,W>; statep = active;Wp := Wp + W

Quiescencep {statep = active}statep := passivesend <dec Wp> to C; Wp := 0

RecoverC receive <dec W> ; RC := RC - Wif RC = 0 then broadcast <term>


Completion by Credit Change

• Construct a static goal dependency graph

• To each strongly connected component of this graph we associate a zone.

• Each zone has table storage controller running an instance of the credit recovery algorithm

• We exchange credits from different zones


Returning to the Example

• We have three zones:– Zone 0 for queries, controller goal manager– Zone 1 for a/1 and b/1, controller T. Storage 2– Zone 2 for c/1, controller T. Storage 1



[0] query([X], b(X), 5)

2. assert(q0(X) b(X) ) [1]

3. call(q0(X), 0) [2]

Prover 1

T. Storage 1

Prover 2

T. Storage 2

4. assert(q0(X) b(X) ) [3]

5. assert(q0(X) b(X) ) [4]

6. table(q0(_), ts1) [5]

7. call(q0(X),0) [6]

10. call(b(X2),t0) [9]

W := [2,5] W := [1,6]

W := [3] W := [4]

W := [6]

RC0=1,2,3,4,5,6

W := [6]

W := [7]

9. call(b(X1),0) [8]

W := [8]

W := [8]W := [8]W := [9]

W := [9]

8. call(q0(X1),t0) [7]

W := [7]

To exchange: [8]

,7,8


Prover 2T. Storage 2

call(a(X3),0) 10

call(a(X4),t1) 11

answer(b(0),t0) 12

call(b(X4),1) 13

answer(a(1),t1) 14

answer(b(0),1) 15

answer(a(1),0) 16

answer(b(1),t0) 17

answer(b(1),1) 18

W := 9,11,12,13,16,18 W := 10,14,15,17,18


Goal Manager

Prover 1

T. Storage 1

T. Storage 2

20. answer(b(0),0) [9]

21. answer(q0(0),t0) [10]

22. answer(q0(0),0) [11]

23. answer(0,5)

24. answer(b(1),0) [10]

25. answer(q0(1),t0) [11]

26. answer(q0(1),0) [12]

27. answer(1,5)

W := [9,11,12,13,16,18]

To exchange: [8]

RC0=1,2,3,4,5,6,7,8

[9]

,10

[10]

,9

RC1= 9,11,12,13,16,18


RC1= 9,11,12,13,16,18

T. Storage 1

Prover 1

Prover 2

29. call(c(0),t1) [20]

33. answer(c(0),2) [21]

28. call(c(0),2) [19]

30. call(c(1),3) [20]

31. call( c(1), t2) [20]

32. answer(c(0),t1) [20]

35. answer(a(0),0)

[23]

34. answer(a(0),t1) [22]

36. answer(b(0),t0) [24]

W := 10,14,15,17,18W := 10,14,15,17,19W:=10,14,15,17,20

To exchange: 19 ,20

RC2= 19, 20

To exchange: [10]

Goal Manager

RC0=1,2,3,4,5,6,7,8,9,10RC0=0RC1= 9,10,11,12,13,14,15,16,17,18,20

T. Storage 2

,21

RC1= 8

W := 22,24

W := 23,24

RC1= 9,10,11,12,13,14,15,16,17,18,19,20,21


Practical Results

• Too bad to be told:

– The current implementation has been done entirely as a Prolog Interpreter over PVM-Prolog.

– The main cause of inefficiency is the (ab)use of asserts/retracts to keep the global state.


Conclusions

• A general and open distributed tabling system was presented.

• Polynomial complexity.

• An extension for completion detection without goal dependency has been introduced.

• Relatively low message overhead.


Goal Manager

Prover 1

T. Storage 1

T. Storage 2

tabling[b(_)] := t0



, (p2,1)

20. answer(b(0),0)

, b(1)

[t0] 0: q0(X1) b(X1)

[t0] q0(0).




solution[t0] := q0(0)

22. answer(q0(0),0)

23. answer(0,5)

24. answer(b(1),0)


[t0] q0(1).

, q0(1)

26. answer(q0(1),0)

27. answer(1,5)

carlos damásiotapd 2000, vigo1 a distributed tabling system carlos viegas damásio...

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