Proceedings. Thirteenth Annual IEEE Conference on Computational Complexity (Formerly: Structure in Complexity Theory Conference) (Cat. No.98CB36247)

18-18 June 1998

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  • Proceedings. Thirteenth Annual IEEE Conference on Computational Complexity (Formerly: Structure in Complexity Theory Conference) (Cat. No.98CB36247)

    Publication Year: 1998
    Request permission for commercial reuse | PDF file iconPDF (188 KB)
    Freely Available from IEEE
  • On membership comparable sets

    Publication Year: 1998, Page(s):2 - 7
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (75 KB)

    A set A is k(n) membership comparable if there is a polynomial time computable function that, given k(n) instances of A of length at most n, excludes one of the 2/sup k(n)/ possibilities for the memberships of the given strings in A. We show that if SAT is O(logn) membership comparable, then UniqueSAT/spl isin/P. This extends the work of previous authors and answers in the affirmative an open ques... View full abstract»

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  • Nonrelativizing separations

    Publication Year: 1998, Page(s):8 - 12
    Cited by:  Papers (22)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (72 KB)

    We show that MA/sub EXP/, the exponential time version of the Merlin-Arthur class, does not have polynomial size circuits. This significantly improves the previous known result due to Kannan since we furthermore show that our result does not relativize. This is the first separation result in complexity theory that does not relativize. As a corollary to our separation result we also obtain that PEX... View full abstract»

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  • Two queries

    Publication Year: 1998, Page(s):13 - 19
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (90 KB)

    We consider the question whether two queries to SAT are as powerful as one query. We show that if P/sup NP[1]/=P/sup NP[2]/ then; locally either NP=coNP or NP has polynomial-size circuits; P/sup NP/=P/sup NP[1]/; /spl Sigma//sub 2//sup p/=UP/sup NP[1]//spl cap/RP/sup NP[1]/; PH=BPP/sup NP[1]/. Moreover we extend work of E. Hemaspaandra et al. (1997) to show that if P(/spl Sigma//sub 2//sup p/[1])=... View full abstract»

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  • Computational indistinguishability: a sample hierarchy

    Publication Year: 1998, Page(s):24 - 33
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (171 KB)

    We consider the existence of pairs of probability ensembles which may be efficiently distinguished from each other given k samples but cannot be efficiently distinguished given k'<k samples. If is well known that in any such pair of ensembles it cannot be that both are efficiently computable (and that such phenomena cannot exist for non-uniform classes of distinguishers, say, polynomial-size ci... View full abstract»

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  • Proofs of membership vs. proofs of knowledge

    Publication Year: 1998, Page(s):34 - 45
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (324 KB)

    We investigate the relationship between interactive proofs of membership and interactive proofs of knowledge. Previous results in this area show that many proofs of membership for some languages are also proofs of knowledge of an associated relation, raising the question of whether all proofs of membership are proofs of knowledge. In this paper we clarify the relationship between these two notions... View full abstract»

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  • Approximating the SVP to within a factor (1-1/dim/sup /spl epsiv//) is NP-hard under randomized conditions

    Publication Year: 1998, Page(s):46 - 55
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (175 KB)

    Recently M. Ajtai showed that to approximate the shortest lattice vector in the l/sub 2/-norm within a factor (1+2(-dim/sup k/)), for a sufficiently large constant k, is NP-hard under randomized reductions. We improve this result to show that to approximate a shortest lattice vector within a factor (1+dim/sup -/spl epsiv//), for any /spl epsiv/>0, is NP-hard under randomized reductions. Our pro... View full abstract»

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  • Arthur-Merlin games in Boolean decision trees

    Publication Year: 1998, Page(s):58 - 67
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (193 KB)

    It is well known that probabilistic boolean decision trees cannot be much more powerful than deterministic ones. Motivated by a question if randomization can significantly speed up a nondeterministic computation via a boolean decision tree, we address structural properties of Arthur-Merlin games in this model and prove some lower bounds. We consider two cases of interest, the first when the length... View full abstract»

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  • On arithmetic branching programs

    Publication Year: 1998, Page(s):68 - 80
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (248 KB)

    We consider the model of arithmetic branching programs, which is a generalization of modular branching programs. We show that, up to a polynomial factor in size, arithmetic branching programs are equivalent to complements of dependency programs. Using this equivalence we prove that dependency programs are closed under conjunction over every field. Furthermore, we show that span programs, an algebr... View full abstract»

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  • The satisfiability problem for probabilistic ordered branching programs

    Publication Year: 1998, Page(s):81 - 90
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (186 KB)

    We show that the satisfiability problem for bounded error probabilistic ordered branching programs is NP-complete. If the error is very small however (more precisely, if the error is bounded by the reciprocal of the width of the branching program), then we have a polynomial-time algorithm for the satisfiability problem. View full abstract»

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  • Isolation, matching, and counting

    Publication Year: 1998, Page(s):92 - 100
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (189 KB)

    We show that the perfect matching problem is in the complexity class SPL (in the nonuniform setting). This provides a better upper bound on the complexity of the matching problem, as well as providing motivation for studying the complexity class SPL. Using similar techniques, we show that the complexity class LogFew coincides with NL in the nonuniform setting. Finally, we provide evidence that our... View full abstract»

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  • A note on the hardness of tree isomorphism

    Publication Year: 1998, Page(s):101 - 105
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (170 KB)

    We prove that the tree isomorphism problem, when trees are encoded as strings, is NC/sup 1/-hard under DLOGTIME-reductions. NC/sup 1/-completeness thus follows from Buss's recent NC/sup 1/ upper bound. By contrast, we prove that testing isomorphism of two trees encoded as pointer lists is L-complete. View full abstract»

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  • Theory of periodically specified problems: complexity and approximability

    Publication Year: 1998, Page(s):106 - 118
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (171 KB)

    We study the complexity and the efficient approximability of graph and satisfiability problems when specified using various kinds of periodic specifications studied previously. We obtain two general results. First, we characterize the complexities of several basic generalized CNF satisfiability problems SAT(S), when instances are specified using various kinds of 1- and 2-dimensional periodic speci... View full abstract»

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  • Models of computation in coding theory

    Publication Year: 1998
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (73 KB)

    In this paper, we contrast some fundamental assumptions of coding theory with those used in complexity theory. In particular, we explain the differences in algorithms used in the software and hardware implementations of Reed-Solomon codes. We also explain how, when studying error-correcting codes, one must consider energy and communication delay to be resources, in addition to the usual space and ... View full abstract»

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  • How to encode a logical structure by an OBDD

    Publication Year: 1998, Page(s):122 - 131
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (316 KB)

    The complexity of problems whose instances are represented by ordered binary decision diagrams (OBDDs) is investigated. By using interleaved variable orders which are well-known in symbolic model checking, we derive hardness results for OBDDs from a Conversion Lemma, extending previous related work about succinct circuit problems and succinct formula problems. This method is applicable for all pro... View full abstract»

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  • Complete problems for promise classes by optimal proof systems for test sets

    Publication Year: 1998, Page(s):132 - 140
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (149 KB)

    We present a uniform approach to investigate the relationship between the existence of complete sets for promise classes and the existence of (p-)optimal proof systems for certain languages. Central to our approach is the notion of a test set which can be used to verify that a given nondeterministic polynomial-time machine obeys the promise on a given input. Basically, we show that a promise class... View full abstract»

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  • Lower bounds for computation with limited nondeterminism

    Publication Year: 1998, Page(s):141 - 152
    Cited by:  Papers (7)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (351 KB)

    We investigate the effect of limiting the number of available nondeterministic bits in different computational models. First we relate formula size to one-way communication complexity and derive lower bounds of /spl Omega/R(n/sup 2-/spl epsiv///log/sup 1-/spl epsiv//n) on the size of formulae with n/sup /spl epsiv///log/sup /spl epsiv//n, nondeterministic bits for 0</spl epsiv//spl les/1/2. Nex... View full abstract»

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  • Solving intractable problems with DNA computing

    Publication Year: 1998, Page(s):154 - 168
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (2101 KB)

    We survey the theoretical use of DNA computing to solve intractable problems. We also discuss the relationship between problems in DNA computing and questions in complexity theory. View full abstract»

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  • Hard sets are hard to find

    Publication Year: 1998, Page(s):170 - 181
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (237 KB)

    We investigate the frequency of complete sets for various complexity classes within EXP under several polynomial-time reductions in the sense of resource bounded measure. We show that these sets are scarce: The sets that are complete under /spl les/(n/sup /spl alpha//-tt/sup -/)/sup P/ reductions for NP, the levels of the polynomial-time hierarchy, and PSPACE have p/sub 2/-measure zero for any con... View full abstract»

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  • On the resource bounded measure of P/poly

    Publication Year: 1998, Page(s):182 - 185
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (88 KB)

    We show that the class of sets having polynomial size circuits, P/poly, has EXP/sup NP/-measure zero under each of the following two assumptions: EXP/sup NP//spl ne/ZPP(/spl Sigma//sub 2//sup p/)(which holds if the polynomial time hierarchy does not collapse to ZPP(/spl Sigma//sub 2//sup p/)), or NP is not small (does not have EXP-measure zero). View full abstract»

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  • Probabilistic martingales and BPTIME classes

    Publication Year: 1998, Page(s):186 - 200
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (215 KB)

    We define probabilistic martingales based on randomized approximation schemes, and show that the resulting notion of probabilistic measure has several desirable robustness properties. Probabilistic martingales can simulate the "betting games" and can cover the same class that a "natural proof" diagonalizes against, as implicitly already shown. The notion would become a full-fledged measure on boun... View full abstract»

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  • Complexity limitations on quantum computation

    Publication Year: 1998, Page(s):202 - 209
    Cited by:  Papers (7)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (110 KB)

    We use the powerful tools of counting complexity and generic oracles to help understand the limitations of the complexity of quantum computation. We show several results for the probabilistic quantum class BQP. BQP is low for PP, i.e., PP/sup BQP/=PP. There exists a relativized world where P=BQP and the polynomial-time hierarchy is infinite. There exists a relativized world where BQP does not have... View full abstract»

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  • Relationships between quantum and classical space-bounded complexity classes

    Publication Year: 1998, Page(s):210 - 227
    Cited by:  Papers (2)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (300 KB)

    This paper investigates the relative power of space-bounded quantum and classical (probabilistic) computational models. The following relationships are proved. 1. Any probabilistic Turing machine (PTM) which runs in space s and which halts absolutely (i.e. halts with certainty after a finite number of steps) can be simulated in space O(s) by a quantum Turing machine (QTM). If the PTM operates with... View full abstract»

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  • Uniformly hard languages

    Publication Year: 1998, Page(s):228 - 234
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (80 KB)

    Ladner (1975) showed that there are no minimal recursive sets under polynomial-time reductions. Given any recursive set A, Ladner constructs a set B such that B strictly reduces to A but B does not lie in P. The set B does have very long sequences of input lengths of easily computable instances. We examine whether Ladner's results hold if we restrict ourselves to "uniformly hard languages" which h... View full abstract»

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  • Resource-bounded measure

    Publication Year: 1998, Page(s):236 - 248
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (237 KB)

    A general theory of resource-bounded measurability and measure is developed. Starting from any feasible probability measure /spl nu/ on the Canter space C (the set of all decision problems) and any suitable complexity class C/spl sube/C, the theory identifies the subsets of C that are /spl nu/-measurable in C and assigns measures to these sets, thereby endowing C with internal measure-theoretic st... View full abstract»

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