Probabilistically Checkable Debate Systems and Nonapproximability of PSPACE-Hard Functions (1993)
| Venue: | Extended abstract in Proc. 25-th ACM Symposium on Theory of Computing |
| Citations: | 29 - 6 self |
BibTeX
@INPROCEEDINGS{Condon93probabilisticallycheckable,
author = {Anne Condon and Joan Feigenbaum and Carsten Lund and Peter Shor},
title = {Probabilistically Checkable Debate Systems and Nonapproximability of PSPACE-Hard Functions},
booktitle = {Extended abstract in Proc. 25-th ACM Symposium on Theory of Computing},
year = {1993},
pages = {305--314},
publisher = {ACM}
}
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Abstract
We initiate an investigation of probabilistically checkable debate systems (PCDS's), a natural generalization of probabilistically checkable proof systems. A PCDS for a language L consists of a probabilistic polynomial-time verifier V and a debate between player 1, who claims that the input x is in L, and player 0, who claims that the input x is not in L. We show that there is a PCDS for L in which V flips O(log n) random coins and reads O(1) bits of the debate if and only if L is in PSPACE. This characterization of PSPACE is used to show that certain PSPACE-hard functions are as hard to approximate closely as they are to compute exactly. 1 Introduction Suppose that two candidates, B and C, agree to a debate format. Voter V is too busy to catch more than a very small number of bits of the debate. How does V decide which of B or C won the debate? In this paper, we show that if These results first appeared in our Technical Memorandum [8]. They were presented in preliminary form at ...
