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Chapter 0: Q12P (page 1)

Let A={M|MisaDFAthatdoesn'tacceptanystringcontaininganoddnumberof1s}Show that Ais decidable.

Short Answer

Expert verified

A is decidable.

Step by step solution

01

Decidable languages

A language is said to be decidable if the inputs of the language is accepted by the Deterministic Finite Automata.

02

Explanation

A language is decidable if the input string of the language is accepted by the Turing Machine. Consider the Turing machine Mthat decides the language A.

The following TM decides A.

鈥淥n input M

  1. Construct a DFA , Dthat accepts every string containing an odd number of 1s.
  2. Construct a DFA, Bsuch that B=LM鈭�LD.
  3. Test whether LB=蠒,using the EDFA decider Tfrom Theorem 4.4.
  4. If Taccepts, accept; if Trejects, reject.鈥�

Therefore, The language

A=M|MisaDFAthatdoesn'tacceptanystringcontaininganoddnumberof1s, is decidable has been proved.

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