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Chapter 9: Q19P (page 390)

Question: LetEREXI^

Short Answer

Expert verified

We know thatPSPACE鈭�EXSPACE i.e., the problem of any EXSPACE-complete cannot be in PSPACE.

Step by step solution

01

Using Regular expression with exponentiation

Consider the statementEREXI^={<R> R is regular expression with exponentiation and

L(R)=鈭�}

From the above statement it can be understood that R is a regular expression and the language, which contains this regular expression consists NULL values.

02

Applying the concept of intractability

EREXI^is said to be intractable because it can be demonstrated in such a manner that is complete for the class EXSPACE.

From the above statements we can conclude that 鈥渁ny EXSPACE-complete problem cannot be in PSPACE and it is much less in P鈥�.

Because PSPACE will be same as EXSPACE which is contradicting the corollary discussed above.

Hence, it can be said thatEREXI^鈭�P

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Most popular questions from this chapter

Show that the language MAX-CLIQUEfrom problem 7.48 isin.PSAT

Describe the error in the following fallacious 鈥減roof鈥� that.P鈮�NPAssume that P=NP and obtain a contradiction. If P=NP, then SAT? P and so, for some k,SAT?TIME(nk)Because every language in NP is polynomial time reducible to SAT, you haveNP鈯�TIME(nk)

. Therefore,.P鈯�TIME(nk)Butby the time hierarchy theorem, TIME(n k+1) contains a language that isn鈥檛 in ,TIME(nk) which contradicts.P鈯�TIME(nk)Therefore, P鈮�NP.

Consider the following function pad:鈭�*脳螡鈫�鈭�*#*that is defined as follows. Let PAD (s, l) = s#3, where j = max (0,l - m) and mis the length of s. Thus, pad (s, l)simply adds enough copies of the new symbol # to the end of s so that the length of the result is at least l. For any language A and function f:N鈫�N, define the language pad(A, f) aspad(A,f)={pad(s,f(m))| where s鈭�Aand 鈥榤鈥� is the length of 鈥榮鈥� }. Prove that if A鈭�TIME(n6), then pad(A,n2)鈭�TIME(n3).

Prove that TIME(2n)鈯�TIME(22n)

Problem 8.13 showedthat ALBAis PSPACE-complete.

a) Do we know whetherALBA鈭�NL?Explain your answer.

b) Do we know whetherALBA鈭�P ?Explain your answer.
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