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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
  • Author index

    Publication Year: 1998, Page(s): 281
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    Freely Available from IEEE
  • A note on the hardness of tree isomorphism

    Publication Year: 1998, Page(s):101 - 105
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (176 KB)

    We prove that the tree isomorphism problem, when trees are encoded as strings, is NC1-hard under DLOGTIME-reductions. NC1 -completeness thus follows from Buss's recent NC1 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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  • Isolation, matching, and counting

    Publication Year: 1998, Page(s):92 - 100
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (196 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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  • Approximating the SVP to within a factor (1-1/dimϵ) 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 (180 KB)

    Recently M. Ajtai showed that to approximate the shortest lattice vector in the l2-norm within a factor (1+2(-dimk)), 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-ε), for any ε>0, is NP-hard under randomized reductions. Ou... 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 (192 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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  • 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 (80 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 2k(n) possibilities for the memberships of the given strings in A. We show that if SAT is O(logn) membership comparable, then UniqueSAT∈P. This extends the work of previous authors and answers in the affirmative an open que... 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 (332 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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  • 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 (256 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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  • Two queries

    Publication Year: 1998, Page(s):13 - 19
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (96 KB)

    We consider the question whether two queries to SAT are as powerful as one query. We show that if PNP[1]=PNP[2] then; locally either NP=coNP or NP has polynomial-size circuits; PNP=PNP[1]; Σ2p=UPNP[1]∩RPNP[1] ; PH=BPPNP[1]. Moreover we extend work of E. Hemaspaandra et al. (1997) to show t... 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 (244 KB)

    A general theory of resource-bounded measurability and measure is developed. Starting from any feasible probability measure ν on the Canter space C (the set of all decision problems) and any suitable complexity class C⊆C, the theory identifies the subsets of C that are ν-measurable in C and assigns measures to these sets, thereby endowing C with internal measure-theoretic structure. Cla... 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 (176 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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  • 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 (308 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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  • Complete problems for promise classes by optimal proof systems for test sets

    Publication Year: 1998, Page(s):132 - 140
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (156 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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  • 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 (176 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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  • 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 (200 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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  • Nonrelativizing separations

    Publication Year: 1998, Page(s):8 - 12
    Cited by:  Papers (14)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (80 KB)

    We show that MAEXP, 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 tha... 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 (88 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&rd... View full abstract»

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  • Resource bounded measure and learnability

    Publication Year: 1998, Page(s):261 - 270
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (156 KB)

    We consider the resource bounded measure of polynomial-time learnable subclasses of polynomial-size circuits. We show that if EXP≠MA, then every PAC-learnable subclass of P/poly has EXP-measure zero. We introduce a nonuniformly computable variant of resource bounded measure and show that, for every fixed polynomial q, any polynomial-time learnable subclass of circuits of size q has measure zero... View full abstract»

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  • Lower bounds for computation with limited nondeterminism

    Publication Year: 1998, Page(s):141 - 152
    Cited by:  Papers (5)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (356 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 ΩR(n2-ε/log1-εn) on the size of formulae with nε/logεn, nondeterministic bits for 0<ε⩽1/2. Next we prove a ... View full abstract»

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  • Complexity limitations on quantum computation

    Publication Year: 1998, Page(s):202 - 209
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (116 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., PPBQP=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... 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 (80 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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  • Complexity issues in Markov decision processes

    Publication Year: 1998, Page(s):272 - 280
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (212 KB)

    We survey the complexity of computational problems about Markov decision processes: evaluating policies, finding good and best policies, approximating best policies, and related decision problems View full abstract»

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  • Randomness is hard

    Publication Year: 1998, Page(s):249 - 260
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (276 KB)

    We study the set of incompressible strings for various resource bounded versions of Kolmogorov complexity. The resource bounded versions of Kolmogorov complexity we study are: polynomial time CD complexity defined by Sipser, the nondeterministic variant due to Buhrman and Fortnow, and the polynomial space bounded Kolmogorov complexity, CS introduced by Hartmanis. For all of these measures we defin... View full abstract»

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  • Solving intractable problems with DNA computing

    Publication Year: 1998, Page(s):154 - 168
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (2108 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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