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Page 1: Complexity...2) Scan the tape and cross off one 0 and one 1, epeat until no 0 or no 1 on the tape, Scan the tape; if a 0 is to the right of a 1, reject n input string s: Consider the

Complexity

Page 2: Complexity...2) Scan the tape and cross off one 0 and one 1, epeat until no 0 or no 1 on the tape, Scan the tape; if a 0 is to the right of a 1, reject n input string s: Consider the

From computability to complexity

mmEnn

47

53 M Byy

it

Page 3: Complexity...2) Scan the tape and cross off one 0 and one 1, epeat until no 0 or no 1 on the tape, Scan the tape; if a 0 is to the right of a 1, reject n input string s: Consider the

From computability to complexity

I t

O

Page 4: Complexity...2) Scan the tape and cross off one 0 and one 1, epeat until no 0 or no 1 on the tape, Scan the tape; if a 0 is to the right of a 1, reject n input string s: Consider the

Time complexity

O nm

rumrunner

tapeO

Page 5: Complexity...2) Scan the tape and cross off one 0 and one 1, epeat until no 0 or no 1 on the tape, Scan the tape; if a 0 is to the right of a 1, reject n input string s: Consider the

Time complexity

2

222sq tbs nm

191 154 191 34 em_

Page 6: Complexity...2) Scan the tape and cross off one 0 and one 1, epeat until no 0 or no 1 on the tape, Scan the tape; if a 0 is to the right of a 1, reject n input string s: Consider the

Big-O cThoI

IIIIns 7ns9

Gcn n3on tn no

Cn 6h3110n

eCon'ton

16h3 eJin

D

Page 7: Complexity...2) Scan the tape and cross off one 0 and one 1, epeat until no 0 or no 1 on the tape, Scan the tape; if a 0 is to the right of a 1, reject n input string s: Consider the

Big-O

OCn3

oe

0Clogin Ougn

YPOY

d

zn0 3

exponentialcomplexity

Page 8: Complexity...2) Scan the tape and cross off one 0 and one 1, epeat until no 0 or no 1 on the tape, Scan the tape; if a 0 is to the right of a 1, reject n input string s: Consider the

Big-O

Ocn's

in C n

0h420cm

11 Hc n nd2

exponentialpolynomial

complexitycomplexity

Page 9: Complexity...2) Scan the tape and cross off one 0 and one 1, epeat until no 0 or no 1 on the tape, Scan the tape; if a 0 is to the right of a 1, reject n input string s: Consider the

ExampleS 000 l l l

lN

O

Iftar.pt nyEeftTInOcn

O p of

0ncleft right Iou

Ocn t Ocn 7 047OCT

Page 10: Complexity...2) Scan the tape and cross off one 0 and one 1, epeat until no 0 or no 1 on the tape, Scan the tape; if a 0 is to the right of a 1, reject n input string s: Consider the

Example151_n E f s 00011 I

O Oln

27106 Isao

104Ocn 10cm.lyn 10cmOcn ligny

Page 11: Complexity...2) Scan the tape and cross off one 0 and one 1, epeat until no 0 or no 1 on the tape, Scan the tape; if a 0 is to the right of a 1, reject n input string s: Consider the

Example Itape a

0

210cm

fanen

e

m E n

0 I Ocn

2 0 I OcnOcn

Page 12: Complexity...2) Scan the tape and cross off one 0 and one 1, epeat until no 0 or no 1 on the tape, Scan the tape; if a 0 is to the right of a 1, reject n input string s: Consider the

Recapnon

regukre

T

500

Page 13: Complexity...2) Scan the tape and cross off one 0 and one 1, epeat until no 0 or no 1 on the tape, Scan the tape; if a 0 is to the right of a 1, reject n input string s: Consider the

Polynomial difference

tin IFnIgn

0

Page 14: Complexity...2) Scan the tape and cross off one 0 and one 1, epeat until no 0 or no 1 on the tape, Scan the tape; if a 0 is to the right of a 1, reject n input string s: Consider the

Time complexity of nondeterministic TM

Twoman9 D

i tHa Ha Ha

1Cs MexftCs7 tis I t Ls

Page 15: Complexity...2) Scan the tape and cross off one 0 and one 1, epeat until no 0 or no 1 on the tape, Scan the tape; if a 0 is to the right of a 1, reject n input string s: Consider the

Exponential differencerun

00

eg tenth

fin DCng fan 20


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