The relativized relationship between probabilistically checkable debate systems, IP and PSPACE

Authors:
Alexander Russell;Ravi Sundaram
Affiliations:
Department of Mathematics, Massachusetts Institute of Technology, 545 Technology Square, Cambridge, MA 02139, USA;Laboratory for Computer Science, Massachusetts Institute of Technology, 545 Technology Square, Cambridge, MA 02139, USA
Venue:
Information Processing Letters
Year:
1995

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Abstract

In 1990, PSPACE was shown to be identical to IP, the class of languages with interactive proofs [18,20]. Recently, PSPACE was again recharacterized, this time in terms of (Random) Probabilistically Checkable Debate Systems [7,8]. In particular, it was shown that PSPACE = PCDS[log n, 1] = RPCDS[log n, 1]. We study the relativized behaviour of the classes defined by these debate systems in comparison with the classes IP and PSPACE. For the relationships between (R)PCDS[r(n), a(n)] and IP and (R) PCDS[r(n), a(n)] and PSPACE we determine a natural boundary (in terms of the parameters r(n) and a(n)) separating direct-simulability and inequality (with probability 1). In addition, we show that if @?O, EXP^O[log n, log n] then P PSPACE.