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Chapter 10: Q7E (page 439)

Show that BPP⊆PSPACE.

Short Answer

Expert verified

We can show thatBPP⊆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∈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’s program but recycling the space used by the previous path.

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

BPP⊆PSPACE

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