Results 1  10
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127
An optimal lower bound on the number of variables for graph identification
 In FOCS
, 1989
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Counting quantifiers, successor relations, and logarithmic space
 J. Comput. Syst. Sci
, 1997
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An Optimal Parallel Algorithm for Formula Evaluation
, 1992
"... A new approach to Buss’s NC¹ algorithm [Proc. 19thACM Symposium on Theory of Computing, Association for Computing Machinery, New York, 1987, pp. 123131] for evaluation of Boolean formulas is presented. This problem is shown to be complete for NC¹ over AC¬ reductions. This approach is then used to s ..."
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Cited by 43 (6 self)
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A new approach to Buss’s NC¹ algorithm [Proc. 19thACM Symposium on Theory of Computing, Association for Computing Machinery, New York, 1987, pp. 123131] for evaluation of Boolean formulas is presented. This problem is shown to be complete for NC¹ over AC¬ reductions. This approach is then used to solve the more general problem of evaluating arithmetic formulas by using arithmetic circuits.
Uniform ConstantDepth Threshold Circuits for Division and Iterated Multiplication
, 2002
"... this paper. 2.1. Circuit Classes We begin by formally defining the three circuit complexity classes that will concern us here. These are given by combinatorial restrictions on the circuits of the family. We will then define the uniformity restrictions we will use. Finally, we will give the equival ..."
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Cited by 41 (8 self)
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this paper. 2.1. Circuit Classes We begin by formally defining the three circuit complexity classes that will concern us here. These are given by combinatorial restrictions on the circuits of the family. We will then define the uniformity restrictions we will use. Finally, we will give the equivalent formulations of uniform circuit complexity classes in terms of descriptive complexity classes
The Complexity of XPath Query Evaluation and XML Typing
 Journal of the ACM
, 2005
"... We study the complexity of two central XML processing problems. The first is XPath 1.0 query processing, which has been shown to be in PTime in previous work. We prove that both the data complexity and the query complexity of XPath 1.0 fall into lower (highly parallelizable) complexity classes, whil ..."
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Cited by 41 (7 self)
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We study the complexity of two central XML processing problems. The first is XPath 1.0 query processing, which has been shown to be in PTime in previous work. We prove that both the data complexity and the query complexity of XPath 1.0 fall into lower (highly parallelizable) complexity classes, while the combined complexity is PTimehard. Subsequently, we study the sources of this hardness and identify a large and practically important fragment of XPath 1.0 for which the combined complexity is LogCFLcomplete and, therefore, in the highly parallelizable complexity class NC 2. The second problem is the complexity of validating XML documents against various typing schemes like Document Type Definitions (DTDs), XML Schema Definitions (XSDs), and tree automata, both with respect to data and to combined complexity. For data complexity, we prove that validation is in LogSpace and depends crucially on how XML data is represented. For the combined complexity, we show that the complexity ranges from LogSpace to LogCFL, depending on the typing scheme.
Relationships Among PL, L, and the Determinant
, 1996
"... Recent results byToda, Vinay, Damm, and Valianthave shown that the complexity of the determinantischaracterized by the complexity of counting the number of accepting computations of a nondeterministic logspacebounded machine. #This class of functions is known as #L.# By using that characterizati ..."
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Cited by 32 (8 self)
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Recent results byToda, Vinay, Damm, and Valianthave shown that the complexity of the determinantischaracterized by the complexity of counting the number of accepting computations of a nondeterministic logspacebounded machine. #This class of functions is known as #L.# By using that characterization and by establishing a few elementary closure properties, we giveavery simple proof of a theorem of Jung, showing that probabilistic logspacebounded #PL# machines lose none of their computational power if they are restricted to run in polynomial time.
Circuit Complexity before the Dawn of the New Millennium
, 1997
"... The 1980's saw rapid and exciting development of techniques for proving lower bounds in circuit complexity. This pace has slowed recently, and there has even been work indicating that quite different proof techniques must be employed to advance beyond the current frontier of circuit lower bound ..."
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Cited by 30 (3 self)
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The 1980's saw rapid and exciting development of techniques for proving lower bounds in circuit complexity. This pace has slowed recently, and there has even been work indicating that quite different proof techniques must be employed to advance beyond the current frontier of circuit lower bounds. Although this has engendered pessimism in some quarters, there have in fact been many positive developments in the past few years showing that significant progress is possible on many fronts. This paper is a (necessarily incomplete) survey of the state of circuit complexity as we await the dawn of the new millennium.
Reducing the Complexity of Reductions
 Computational Complexity
, 1997
"... We prove that the BermanHartmanis isomorphism conjecture is true under AC 0 reductions. More generally, we show three theorems that hold for any complexity class C closed under (uniform) TC 0 computable manyone reductions. Isomorphism: The sets complete for C under AC 0 reductions are all i ..."
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Cited by 30 (13 self)
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We prove that the BermanHartmanis isomorphism conjecture is true under AC 0 reductions. More generally, we show three theorems that hold for any complexity class C closed under (uniform) TC 0 computable manyone reductions. Isomorphism: The sets complete for C under AC 0 reductions are all isomorphic under isomorphisms computable and invertible by AC 0 circuits of depth three. Gap: The sets that are complete for C under AC 0 and NC 0 reducibility coincide. Stop Gap: The sets that are complete for C under AC 0 [mod 2] and AC 0 reducibility do not coincide. (These theorems hold both in the nonuniform and Puniform settings.) To prove the second theorem for Puniform settings, we show how to derandomize a version of the switching lemma, which may be of independent interest. (We have recently learned that this result is originally due to Ajtai and Wigderson, but it has not been published.) 1 Introduction The notion of complete sets in complexity classes provides one of ...
Reductions in Circuit Complexity: An Isomorphism Theorem and a Gap Theorem
 Journal of Computer and System Sciences
"... We show that all sets that arecomplete for NP under nonuniform AC are isomorphic under nonuniform AC computable isomorphisms. Furthermore, these sets remain NPcomplete even under nonuniform NC reductions. ..."
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Cited by 29 (11 self)
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We show that all sets that arecomplete for NP under nonuniform AC are isomorphic under nonuniform AC computable isomorphisms. Furthermore, these sets remain NPcomplete even under nonuniform NC reductions.
The Permanent Requires Large Uniform Threshold Circuits
, 1999
"... We show that the permanent cannot be computed by uniform constantdepth threshold circuits of size T (n) for any function T such that for all k, T (k) (n) = o(2 n ). More generally, we show that any problem that is hard for the complexity class C=P requires circuits of this size (on the unif ..."
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Cited by 28 (8 self)
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We show that the permanent cannot be computed by uniform constantdepth threshold circuits of size T (n) for any function T such that for all k, T (k) (n) = o(2 n ). More generally, we show that any problem that is hard for the complexity class C=P requires circuits of this size (on the uniform constantdepth threshold circuit model). In particular, this lower bound applies to any problem that is hard for the complexity classes PP or #P.