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The Boolean formula value problem is in ALOGTIME
 in Proceedings of the 19th Annual ACM Symposium on Theory of Computing
, 1987
"... The Boolean formula value problem is in alternating log time and, more generally, parenthesis contextfree languages are in alternating log time. The evaluation of reverse Polish notation Boolean formulas is also in alternating log time. These results are optimal since the Boolean formula value ..."
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Cited by 68 (7 self)
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The Boolean formula value problem is in alternating log time and, more generally, parenthesis contextfree languages are in alternating log time. The evaluation of reverse Polish notation Boolean formulas is also in alternating log time. These results are optimal since the Boolean formula value problem is complete for alternating log time under deterministic log time reductions. Consequently, it is also complete for alternating log time under AC reductions.
On TruthTable Reducibility to SAT
, 2002
"... We show that polynomial time truthtable reducibility via Boolean circuits to SAT is the same as logspace truthtable reducibility via Boolean formulas to SAT and the same as logspace Turing reducibility to SAT . In addition, we prove that a constant number of rounds of parallel queries to SAT i ..."
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Cited by 50 (2 self)
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We show that polynomial time truthtable reducibility via Boolean circuits to SAT is the same as logspace truthtable reducibility via Boolean formulas to SAT and the same as logspace Turing reducibility to SAT . In addition, we prove that a constant number of rounds of parallel queries to SAT is equivalent to one round of parallel queries.
Complexity Models for Incremental Computation
, 1994
"... We present a new complexity theoretic approach to incremental computation. We define complexity classes that capture the intuitive notion of incremental efficiency and study their relation to existing complexity classes. We show that problems that have small sequential space complexity also have sma ..."
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Cited by 42 (4 self)
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We present a new complexity theoretic approach to incremental computation. We define complexity classes that capture the intuitive notion of incremental efficiency and study their relation to existing complexity classes. We show that problems that have small sequential space complexity also have small incremental time complexity. We show that all common LOGSPACEcomplete problems for P are also incrPOLYLOGTIMEcomplete for P. We introduce a restricted notion of completeness called NRPcompleteness and show that problems which are NRPcomplete for P are also incrPOLYLOGTIMEcomplete for P. We also give incrementally complete problems for NLOGSPACE, LOGSPACE, and nonuniform NC¹. We show that under certain restrictions problems which have efficient dynamic solutions also have efficient parallel solutions. We also consider a nonuniform model of incremental computation and show that in this model most problems have almost linear complexity. In addition, we present some techniques f...
Playing with Boolean blocks, part I: Post’s lattice with applications to complexity theory
 SIGACT News
"... Let us imagine children playing with a box containing a large number of building blocks such as LEGO TM, fischertechnik ® , Polydron, or something similar. Each block belongs to a certain class (given by, e. g., color, shape, or size) and usually the number of different such classes is relatively sm ..."
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Cited by 40 (12 self)
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Let us imagine children playing with a box containing a large number of building blocks such as LEGO TM, fischertechnik ® , Polydron, or something similar. Each block belongs to a certain class (given by, e. g., color, shape, or size) and usually the number of different such classes is relatively small. It is amazing to see how involved the constructions are that can be built by the kids. From
Computing Functions with Parallel Queries to NP
, 1993
"... The class \Theta p 2 of languages polynomialtime truthtable reducible to sets in NP has a wide range of different characterizations. We consider several functional versions of \Theta p 2 based on these characterizations. We show that in this way the three function classes FL NP log , FP NP l ..."
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Cited by 39 (1 self)
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The class \Theta p 2 of languages polynomialtime truthtable reducible to sets in NP has a wide range of different characterizations. We consider several functional versions of \Theta p 2 based on these characterizations. We show that in this way the three function classes FL NP log , FP NP log , and FP NP k are obtained. In contrast to the language case the function classes seem to all be different. We give evidence in support of this fact by showing that FL NP log coincides with any of the other classes then L = P, and that the equality of the classes FP NP log and FP NP k would imply that the number of nondeterministic bits needed for the computation of any problem in NP can be reduced by a polylogarithmic factor, and that the problem can be computed deterministically with a subexponential time bound of order 2 n O(1= log log n) . 1 Introduction The study of nondeterministic computation is a central topic in structural complexity theory. The acceptance mechanism of...
Efficient Parallel Evaluation of Straightline Code and Arithmetic Circuits
 SIAM J. Comput
, 1988
"... A new parallel algorithm is given to evaluate a straight line program. The algorithm evaluates a program over a commutative semiring R of degree d and size n in time O(log n(log nd)) using M(n) processors, where M(n) is the number of processors required for multiplying n \Theta n matrices over the ..."
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Cited by 32 (5 self)
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A new parallel algorithm is given to evaluate a straight line program. The algorithm evaluates a program over a commutative semiring R of degree d and size n in time O(log n(log nd)) using M(n) processors, where M(n) is the number of processors required for multiplying n \Theta n matrices over the semiring R in O(log n) time. Appears in SIAM J. Comput., 17/4, pp. 687695 (1988). Preliminary version of this paper appeared in [6]. y Research supported in part by National Science Foundation Grant MCS800756 A01. z Research supported by NSF under ECS8404866, the Semiconductor Research Corporation under RSCH 84060496, and by an IBM Faculty Development Award. x Research Supported in part by NSF Grant DCR8504391 and by an IBM Faculty Development Award. 1 INTRODUCTION 1 1 Introduction In this paper we consider the problem of dynamic evaluation of a straight line program in parallel. This is a generalization of the result of Valiant et al [10]. They consider the problem of ta...
The complexity of type inference for higherorder typed lambda calculi
 In. Proc. 18th ACM Symposium on the Principles of Programming Languages
, 1991
"... We analyse the computational complexity of type inference for untyped X,terms in the secondorder polymorphic typed Xcalculus (F2) invented by Girard and Reynolds, as well as higherorder extensions F3,F4,...,/ ^ proposed by Girard. We prove that recognising the i^typable terms requires exponential ..."
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Cited by 28 (11 self)
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We analyse the computational complexity of type inference for untyped X,terms in the secondorder polymorphic typed Xcalculus (F2) invented by Girard and Reynolds, as well as higherorder extensions F3,F4,...,/ ^ proposed by Girard. We prove that recognising the i^typable terms requires exponential time, and for Fa the problem is nonelementary. We show as well a sequence of lower bounds on recognising the i^typable terms, where the bound for Fk+1 is exponentially larger than that for Fk. The lower bounds are based on generic simulation of Turing Machines, where computation is simulated at the expression and type level simultaneously. Nonaccepting computations are mapped to nonnormalising reduction sequences, and hence nontypable terms. The accepting computations are mapped to typable terms, where higherorder types encode reduction sequences, and firstorder types encode the entire computation as a circuit, based on a unification simulation of Boolean logic. A primary technical tool in this reduction is the composition of polymorphic functions having different domains and ranges. These results are the first nontrivial lower bounds on type inference for the Girard/Reynolds
Are there Hard Examples for Frege Systems?
"... It is generally conjectured that there is an exponential separation between Frege and extended Frege systems. This paper reviews and introduces some candidates for families of combinatorial tautologies for which Frege proofs might need to be superpolynomially longer than extended Frege proofs. S ..."
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Cited by 20 (2 self)
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It is generally conjectured that there is an exponential separation between Frege and extended Frege systems. This paper reviews and introduces some candidates for families of combinatorial tautologies for which Frege proofs might need to be superpolynomially longer than extended Frege proofs. Surprisingly, we conclude that no particularly good or convincing examples are known. The examples of combinatorial tautologies that we consider seem to give at most a quasipolynomial speedup of extended Frege proofs over Frege proofs, with the sole possible exception of tautologies based on a theorem of Frankl. It is
ComplexityTheoretic Aspects of Interactive Proof Systems
, 1989
"... In 1985, Goldwasser, Micali and Rackoff formulated interactive proof systems as a tool for developing cryptographic protocols. Indeed, many exciting cryptographic results followed from studying interactive proof systems and the related concept of zeroknowledge. Interactive proof systems also have a ..."
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Cited by 19 (3 self)
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In 1985, Goldwasser, Micali and Rackoff formulated interactive proof systems as a tool for developing cryptographic protocols. Indeed, many exciting cryptographic results followed from studying interactive proof systems and the related concept of zeroknowledge. Interactive proof systems also have an important part in complexity theory merging the well established concepts of probabilistic and nondeterministic computation. This thesis will study the complexity of various models of interactive proof systems. A perfect zeroknowledge interactive protocol convinces a verifier that a string is in a language without revealing any additional knowledge in an information theoretic sense. This thesis will show that for any language that has a perfect zeroknowledge proof system, its complement has a short interactive protocol. This result implies that there are not any perfect zeroknowledge protocols for NPcomplete languages unless the polynomialtime hierarchy collapses. Thus knowledge comp...
An overview of computational complexity
 Communications of the ACM
, 1983
"... foremost recognition of technical contributions to the computing community. The citation of Cook's achievements noted that "Dr. Cook has advanced our understanding of the complexity of computation in a significant and profound way. His seminal paper, The Complexity of Theorem Proving Procedures ..."
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Cited by 18 (0 self)
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foremost recognition of technical contributions to the computing community. The citation of Cook's achievements noted that "Dr. Cook has advanced our understanding of the complexity of computation in a significant and profound way. His seminal paper, The Complexity of Theorem Proving Procedures, presented at the 1971 ACM SIGACT Symposium on the Theory of Computing, laid the foundations for the theory of NPcompleteness. The ensuing exploration of the boundaries and nature of the NPcomplete class of problems has been one of the most active and important research activities in computer science for the last decade. Cook is well known for his influential results in fundamental areas of computer science. He has made significant contributions to complexity theory, to timespace tradeoffs in computation, and to logics for programming languages. His work is characterized by elegance and insights and has illuminated the very nature of computation." During 19701979, Cook did extensive work under grants from the