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Chapter 7: Q10E (page 323)

Show that ALLDFAisinP.

Short Answer

Expert verified

The ALLDFAisin showed.

Step by step solution

01

Step 1:To Randomized the Class - P

On such a randomized single-tap Turing machine, P is indeed a class of languages that can be answered in polynomial time.

ALLDFA={<A>AisaDFAthatrecognies\mathop鈭�*}

EDFA={<A>AisaDFAandLA=鈭�}

is determined by a Turing 鈥� machine (TM)

Let E be the Turing machine that determinesEDFA

Let R be the Turing machine that determines ALLDFA

02

The R – Algorithm Steps

The algorithm of R is as follows:

:R=''Oninput<A>,whereAisaDFA

1. Construct a DFA鈥�Bthat recognizesL(A炉), by swapping accept and non 鈥� accepting states

2. Run the TMEon input<B>, where E determinesEDFA.

3. If E accepts, then accept

4. If E rejects, then reject.鈥�

Clearly theTMR determinesALLDFA in polynomial time.Therefore, ALLDFAis in P.

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