Introduction to the Theory of ComputationDiscusses such topics as: regular languages; context-free languages; Church-Turing thesis; decidability; reducibility; the recursion theorem; time complexity; space complexity; and provable intractability. |
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Page 116
... reject state and rejecting , or by looping . Sometimes distinguishing between a machine that is looping from one that is merely taking a long time is difficult . For this reason we prefer Turing machines that halt on all inputs ; such ...
... reject state and rejecting , or by looping . Sometimes distinguishing between a machine that is looping from one that is merely taking a long time is difficult . For this reason we prefer Turing machines that halt on all inputs ; such ...
Page 147
... rejects if M fails . to accept w . In other words , H ( { M , w ) ) = accept reject if M accepts w if M does not accept w . Now we construct a new Turing machine D with H as a subroutine . This new TM calls H to determine what M does ...
... rejects if M fails . to accept w . In other words , H ( { M , w ) ) = accept reject if M accepts w if M does not accept w . Now we construct a new Turing machine D with H as a subroutine . This new TM calls H to determine what M does ...
Page 148
... reject , since H rejects input ( M3 , ( M2 ) ) . ( M1 ) ( M2 ) ( M3 ) ( M4 ) M1 accept reject M2 accept accept accept M3 reject reject reject M4 accept accept reject accept reject accept reject reject FIGURE 4.7 Entry i , j is the value ...
... reject , since H rejects input ( M3 , ( M2 ) ) . ( M1 ) ( M2 ) ( M3 ) ( M4 ) M1 accept reject M2 accept accept accept M3 reject reject reject M4 accept accept reject accept reject accept reject reject FIGURE 4.7 Entry i , j is the value ...
Contents
Formal definition of a nondeterministic finite automaton | 1 |
Proof by construction | 19 |
Regular Languages | 29 |
Copyright | |
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Common terms and phrases
A₁ accepting computation history alphabet arrows automata binary Boolean C₁ called Chomsky normal form clause configuration construct contains context-free grammar context-free language convert corresponding decidable language decide ATM defined describe deterministic diagram directed graph domino edges empty stack encoding enumerable EQTM equivalent example finite automaton following figure formal definition GNFA graph G halts HAMPATH induction input string integers label length M2 accepts machine accepts mapping reducibility match mathematical N₁ nodes nondeterminism nondeterministic finite nondeterministic finite automaton nondeterministic Turing machine notation NP-complete output pair parse tree polynomial polynomial time algorithm polynomial time reducible PROOF IDEA prove pumping lemma pushdown automaton q₁ recursion theorem regular expression regular languages reject rule running SAN DIEGO satisfying assignment Scan sequence simulate single-tape Stage steps SUBSET-SUM substring tape transition function true Turing machine undecidable variable write