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Chapter 10: Q7E (page 439)

Show that BPP鈯�PSPACE.

Short Answer

Expert verified

We can show thatBPP鈯�PSPACE by converting BPP into PSPACE.

Step by step solution

01

Understanding and solving the problem using polynomial time

Consider M be a probabilistic TM which runs on polynomial time.

Therefore, .M鈭�BPP can be modified so that M makes exactlyac coin tosses in each branch of its computation, for any constant C

02

Understanding the performing of the task

Since, there are total of2(a0) computation path, problem which is determining probability that M accepts its input is reduces to counting how many branches B are accepting and comparing this number withp=(34).2(a0)

If,then accept otherwise reject. Now the given deterministic task can be performed in the polynomial space by generating all possible paths sequentially following M鈥檚 program but recycling the space used by the previous path.

Therefore, the problem of BPP is converted into PSPACE. Hence,

BPP鈯�PSPACE

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Most popular questions from this chapter

A k-head pushdown automaton (k-PDA) is a deterministic pushdown automaton with k read-only, two-way input heads and a read/write stack. Define the class PDAK={AA is recognised by a k-PDA}. Show that p=UkPDAk. (Hint: Recall that P equals alternating log space.)

A Boolean formula is a Boolean Circuit wherein every gate has only one output wire. The same input variable may appear in multiple places of a Boolean Formula. Prove that a language has a polynomial size family of formulas if it is in NC1. Ignore uniformity considerations.

Show that ifNP鈯�BPP,then.NP=RP

Show that any function with n inputs can be computed by a branching program that has O(2n)nodes.

Let A be a regular language over{0,1} . Show that A has size-depth complexity(O(n).O(logn)).
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