Random Debaters and the Hardness of Approximating Stochastic Functions

A probabilistically checkable debate system (PCDS) for a language L consists of a probabilisticpolynomial-time veri er 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. It is known that there is a PCDS for L in which V ips O(logn) coins and reads O(1) bits of the debate if and only if L is in PSPACE ( Condon et al., Proc. 25th ACM Symposiumon Theory of Computing, 1993, pp. 304{315]). In this paper, we restrict attention to RPCDS's, which are PCDS's in which Player 0 follows a very simple strategy: On each turn, Player 0 chooses uniformly at random from the set of legal moves. We prove the following result. Theorem: L has an RPCDS in which the veri er ips O(logn) coins and reads O(1) bits of the debate if and only if L is in PSPACE. This new characterizationof PSPACE is used toshow thatcertainstochastic PSPACE-hardfunctions are as hardto approximatecloselyas they areto computeexactly. Examplesof such fu...

• Type: Conference
• Year: 1994
• Where: COCO
• Authors: Anne Condon, Joan Feigenbaum, Carsten Lund, Peter W. Shor
• Keywords: Algorithms, COCO 1994, Probabilisticpolynomial-time Veri Er, Veri Er, Veri Er Ips