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Chapter 8: Q5E (page 357)

Show that ADFA∈L

Short Answer

Expert verified

The space required to run this simulation is O(logn).

Step by step solution

01

Step-1: DFA

LetADFAbe the language

{ (A,w)| A is a DFA that accepts W }

where (A,w)denotes the encoding of A followed by W.

02

Step-2: To explain turning machine 

To decideADFA, build a turning machine (TM).

When M takes (A,w), a DFA and a string M as input, it performs A on W by keeping track of A's current state and its current head location and updating them as needed.

Because M may be recorded simply placing a pointer into its input, the space required to run this simulation is O(logn).

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Most popular questions from this chapter

Consider the following generalized geography game wherein the start node is the one with the arrow pointing in from nowhere. Does Player I have a winning strategy? Does Player II? Give reasons for your answers.

LetMULT={a#b#c|a,b,care binary natural numbers and a×b=c}. Showthat MULT∈L.

Define ALBA={M,wMis an LBA that accepts input w}. Show that is PSPACE-complete.

For any positive integer x, let xR be the integer whose binary representation isthe reverse of the binary representation of x. (Assume no leading in the binary representation of x.) Define the function R+:N→NwhereR+(x)=x+xR.
a. Let A2=⟨x,y⟩|R+(x)=y.

ShowA2∈L.
b. Let A2=⟨x,y⟩|R+(R+(x))=y. ShowA3∈L.

A ladderis a sequence of strings s1, s2, . . . ,sk, wherein every string differs from the preceding one by exactly one character. For example, the following is a ladder of English words, starting with “head” and ending with “free”:head, hear, near, fear, bear, beer, deer, deed, feed, feet, fret, free.

Let

LADDERDFA={(M,s,t)|MisaDFAandL(M) containsaladderofstrings,startingwithsandendingwitht}

Show that LADDERDFA is in PSPACE.
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