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Designing Programs That Check Their Work
, 1989
"... A program correctness checker is an algorithm for checking the output of a computation. That is, given a program and an instance on which the program is run, the checker certifies whether the output of the program on that instance is correct. This paper defines the concept of a program checker. It d ..."
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Cited by 307 (17 self)
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A program correctness checker is an algorithm for checking the output of a computation. That is, given a program and an instance on which the program is run, the checker certifies whether the output of the program on that instance is correct. This paper defines the concept of a program checker. It designs program checkers for a few specific and carefully chosen problems in the class FP of functions computable in polynomial time. Problems in FP for which checkers are presented in this paper include Sorting, Matrix Rank and GCD. It also applies methods of modern cryptography, especially the idea of a probabilistic interactive proof, to the design of program checkers for group theoretic computations. Two strucural theorems are proven here. One is a characterization of problems that can be checked. The other theorem establishes equivalence classes of problems such that whenever one problem in a class is checkable, all problems in the class are checkable.
On the complexity of space bounded interactive proofs
 In 30th Annual Symposium on Foundations of Computer Science
, 1989
"... Some of the most exciting developments in complexity theory in recent years concern the complexity of interactive proof systems, defined by Goldwasser, Micali and Rackoff (1985) and independently by Babai (1985). In this paper, we survey results on the complexity of space bounded interactive proof s ..."
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Cited by 54 (5 self)
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Some of the most exciting developments in complexity theory in recent years concern the complexity of interactive proof systems, defined by Goldwasser, Micali and Rackoff (1985) and independently by Babai (1985). In this paper, we survey results on the complexity of space bounded interactive proof systems
PSPACE Is Provable By Two Provers In One Round
, 1991
"... We show that every language in PSPACE, or equivalently every language accepted by an unbounded round interactive proof system, has a 1round, 2prover interactive proof system with exponentially small error probability. To obtain this result, we prove the correctness of a simple but powerful method ..."
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Cited by 18 (0 self)
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We show that every language in PSPACE, or equivalently every language accepted by an unbounded round interactive proof system, has a 1round, 2prover interactive proof system with exponentially small error probability. To obtain this result, we prove the correctness of a simple but powerful method for parallelizing 2prover interactive proof systems to reduce their error. 1 Introduction We describe a general methodology for parallelizing unbounded round interactive proof systems to obtain 1round, 2prover interactive proof systems. We show that this methodology yields a 1round, 2prover interactive proof system for any language in PSPACE. Our interactive proof systems have exponentially small error probability. The notion of a singleprover interactive proof system was introduced by Goldwasser, Micali and Rackoff [12] and by Babai [1] and was generalized to two and more provers by BenOr, Goldwasser, Kilian and Wigderson [5]. In a singleprover interactive proof system, a prover...
On the Structure of LogSpace Probabilistic Complexity Classes
, 1994
"... We investigate hierarchical properties and logspace reductions of languages recognized by logspace probabilistic Turing machines, ArthurMerlin games and Games against Nature with logspace probabilistic verifiers. For each logspace complexity class, we decompose it into a hierarchy based on corr ..."
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Cited by 1 (1 self)
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We investigate hierarchical properties and logspace reductions of languages recognized by logspace probabilistic Turing machines, ArthurMerlin games and Games against Nature with logspace probabilistic verifiers. For each logspace complexity class, we decompose it into a hierarchy based on corresponding multihead twoway finite automata and we (eventually) prove the separation of the hierarchy levels (even over one letter alphabet); furthermore, we show logspace reductions of each logspace complexity class to low levels of its corresponding hierarchy. We find probabilistic (and "probabilistic+nondeterministic") variants of Savitch's maze threading problem which are logspace complete for PL (and respectively P) and can be recognized by twohead oneway and oneway onecounter finite automata with probabilistic (probabilistic and nondeterministic) states. This research was supported by the National Science Foundation under Grant No. CDA 8822724. 1 Results We focus on classes d...