Pspace-hard Functions Checkable Debate Systems and Approximation Algorithms for Pspace

to use journal articles in a variety of ways, limited only as required to insure fair attribution to authors and the journal, and to prohibit use in a competing commercial product. See the journal's World Wide Web site for further details. The Chicago Journal of Theoretical Computer Science is a peer-reviewed scholarly journal in theoretical computer science. The journal is committed to providing a forum for signiicant results on theoretical aspects of all topics in computer science. Abstract We initiate an investigation of probabilistically checkable debate Abstract-1 systems (PCDS), a natural generalization of probabilistically check-able proof systems (PCPS). A PCDS for a language L consists of a probabilistic polynomial-time veriier 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 ips 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.Hard Functionss CFLS93b].