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 54
... PROOF IDEA We have regular languages A1 and A2 and want to prove that A1 U A2 is regular . The idea is to take two NFAS , N1 and N2 for A1 and A2 , and combine them into one new NFA , N. Machine N must accept its input if either N1 or ...
... PROOF IDEA We have regular languages A1 and A2 and want to prove that A1 U A2 is regular . The idea is to take two NFAS , N1 and N2 for A1 and A2 , and combine them into one new NFA , N. Machine N must accept its input if either N1 or ...
Page 155
... proofs that demonstrate the reducibility method for proving undecidability . Let ETM = { ( M ) | M is a TM and L ( M ) = 0 } . THEOREM 5.2 ETM is undecidable . PROOF IDEA We follow the pattern adopted in Theorem 5.1 . We assume for the ...
... proofs that demonstrate the reducibility method for proving undecidability . Let ETM = { ( M ) | M is a TM and L ( M ) = 0 } . THEOREM 5.2 ETM is undecidable . PROOF IDEA We follow the pattern adopted in Theorem 5.1 . We assume for the ...
Page 157
Michael Sipser. THEOREM 5.3 REGULARTM is undecidable . PROOF IDEA As usual for undecidability theorems , this proof is by reduction from ATM . We assume that REGULAR ... PROOF IDEA Show that 5.1 UNDECIDABLE PROBLEMS FROM LANGUAGE THEORY 157.
Michael Sipser. THEOREM 5.3 REGULARTM is undecidable . PROOF IDEA As usual for undecidability theorems , this proof is by reduction from ATM . We assume that REGULAR ... PROOF IDEA Show that 5.1 UNDECIDABLE PROBLEMS FROM LANGUAGE THEORY 157.
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