Chapter 0: Q12P (page 1)

Let $A = {\{M\} | M i s a D F A t h a t d o e s n' t a c c e p t a n y s t r i n g c o n t a i n i n g a n o d d n u m b e r o f 1 s}$ Show that $A$ is decidable.

Short Answer

Expert verified

A is decidable.

Step by step solution

Decidable languages

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

Explanation

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

The following TM decides A.

“On input $<M>$

Construct a DFA , $D$ that accepts every string containing an odd number of 1s.
Construct a DFA, $B$ such that $(B) = L (M) \cap L (D)$ .
Test whether $L (B) = ϕ$ ,using the E_DFA decider $T$ from Theorem 4.4.
If $T$ accepts, accept; if $T$ rejects, reject.”

Therefore, The language

$A = \{\{M\} | M i s a D F A t h a t d o e s n' t a c c e p t a n y s t r i n g c o n t a i n i n g a n o d d n u m b e r o f 1 s\}$ , is decidable has been proved.

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Let $A = {\{M\} | M i s a D F A t h a t d o e s n' t a c c e p t a n y s t r i n g c o n t a i n i n g a n o d d n u m b e r o f 1 s}$ Show that $A$ is decidable.

Short Answer

Step by step solution

Decidable languages

Explanation

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

Short Answer

Step by step solution

Decidable languages

Explanation

One App. One Place for Learning.

Most popular questions from this chapter

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Let $A = {\{M\} | M i s a D F A t h a t d o e s n' t a c c e p t a n y s t r i n g c o n t a i n i n g a n o d d n u m b e r o f 1 s}$ Show that $A$ is decidable.