Proceedings of Computational Complexity (Formerly Structure in Complexity Theory)

24-27 May 1996

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  • Proceedings of Computational Complexity (Formerly Structure in Complexity Theory)

    Publication Year: 1996
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    Freely Available from IEEE
  • Author index

    Publication Year: 1996
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    Freely Available from IEEE
  • Parallel complexity hierarchies based on PRAMs and DLOGTLME-uniform circuits

    Publication Year: 1996, Page(s):24 - 32
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (668 KB)

    Unlike the case of logspace-uniform circuits, complexity hierarchies do exist for PRAMs and DLOGTIME-uniform circuits: (i) There exist a constant d and a language L such that L is recognizable in time dT(n) by some PRIORITY CRCW PRAM but is not recognizable in time T(n) by any PRIORITY CRCW PRAM if the number of processors is fixed. (ii) There exist constants c, d and a language L such that L is r... View full abstract»

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  • On coherence, random-self-reducibility, and self-correction

    Publication Year: 1996, Page(s):59 - 67
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (688 KB)

    We address two questions about self-reducibility-the power of adaptiveness in examiners that take advice and the relationship between random-self-reducibility and self-correctability. We first show that adaptive examiners are more powerful than nonadaptive examiners, even if the nonadaptive ones are nonuniform. Blum et al. (1993) showed that every random-self-reducible function is self-correctable... View full abstract»

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  • Integer programming as a framework for optimization and approximability

    Publication Year: 1996, Page(s):249 - 259
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (884 KB)

    Structural approximation theory seeks to provide a framework for expressing optimization problems, and isolating structural or syntactic conditions that explain the (apparent) difference in the approximation properties of different NP-optimization problems. In this paper, we initiate a study of structural approximation using integer programming (an optimization problem in its own right) as a gener... View full abstract»

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  • Reducing P to a sparse set using a constant number of queries collapses P to L

    Publication Year: 1996, Page(s):88 - 96
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (620 KB)

    We prove that there is no sparse hard set for P under logspace computable bounded truth-table reductions unless P=L. In case of reductions computable in NC1, the collapse goes down to P=NC 1. We generalize this result by parameterizing the sparseness condition, the space bound and the number of queries of the reduction, apply the proof technique to NL and L, and extend all th... View full abstract»

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  • Nondeterministic NC1 computation

    Publication Year: 1996, Page(s):12 - 21
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    We define the counting classes NC1, GapNC1 PNC1 and C=NC1. We prove that Boolean circuits, algebraic circuits, programs over nondeterministic finite automata, and programs over constant integer matrices yield equivalent definitions of the latter three classes. We investigate closure properties. We observe that NC1⊆L and that C<... View full abstract»

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  • Randomization and derandomization in space-bounded computation

    Publication Year: 1996, Page(s):128 - 149
    Cited by:  Papers (11)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (1936 KB)

    This is a survey of spacebounded probabilistic computation, summarizing the present state of knowledge about the relationships between the various complexity classes associated with such computation. The survey especially emphasizes recent progress in the construction of pseudorandom generators that fool probabilistic space-bounded computations, and the application of such generators to obtain det... View full abstract»

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  • Extracting randomness: how and why. A survey

    Publication Year: 1996, Page(s):44 - 58
    Cited by:  Papers (22)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (1172 KB)

    Extractors are Boolean functions that allow, in some precise sense, extraction of randomness from somewhat random distributions. Extractors, and the closely related “Dispersers”, exhibit some of the most “random-like” properties of explicitly constructed combinatorial structures. In turn, extractors and dispersers have many applications in “removing randomness” ... View full abstract»

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  • Truth-table closure and Turing closure of average polynomial time have different measures in EXP

    Publication Year: 1996, Page(s):190 - 195
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (456 KB)

    Let PP-comp denote the sets that are solvable in polynomial time on average under every polynomial time computable distribution on the instances. In this paper we show that the truth-table closure of PP-comp has measure 0 in EXP. Since, as we show, EXP is Turing reducible to PP-comp, the Turing closure has measure 1 in EXP and thus, PP-comp is an example... View full abstract»

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  • The complexity of knowledge representation

    Publication Year: 1996, Page(s):244 - 248
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (424 KB)

    Representing knowledge in forms appropriate for rapid common-sense reasoning is a challenging current problem in artificial intelligence. We review certain recent results which suggest that complexity theory has an important role to play in this field View full abstract»

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  • VC dimension in circuit complexity

    Publication Year: 1996, Page(s):81 - 85
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (344 KB)

    The main result of this paper is a Ω(n1/4) lower bound on the size of a sigmoidal circuit computing a specific AC2 0 function. This is the first lower bound for the computation model of sigmoidal circuits with unbounded weights. We also give upper and lower bounds for the same function in a few other computation models: circuits of AND/OR gates, threshold cir... View full abstract»

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  • An isomorphism theorem for circuit complexity

    Publication Year: 1996, Page(s):2 - 11
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (872 KB)

    We show that all sets complete for NC1 under AC0 reductions are isomorphic under AC0-computable isomorphisms. Although our proof does not generalize directly to other complexity classes, we do show that, for all complexity classes C closed under NC1-computable many-one reductions, the sets complete for C under NC0 reductions are all isomorphi... View full abstract»

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  • Succinct representation, leaf languages, and projection reductions

    Publication Year: 1996, Page(s):118 - 126
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (728 KB)

    The concepts of succinct problem representation, and of NP leaf languages, were developed to characterize complexity classes above polynomial time. Here, we work out a descriptive complexity approach to succinctly represented problems, and prove a strictly stronger version of the Conversion Lemma from Balcazar et al (1992) which allows iterated application. Moreover, we prove that for every proble... View full abstract»

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  • A comparison of weak completeness notions

    Publication Year: 1996, Page(s):171 - 178
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (620 KB)

    We compare the weak completeness notions for E in the sense of Lutz's resource-bounded measure theory (1992) with respect to the standard polynomial time reducibilities. Our results parallel results for classical completeness by Watanabe (1987) and others. We show that the weak completeness notions for 1-query reductions coincide: A set is weakly complete for E under 1-truth-table reducibility iff... View full abstract»

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  • A note on p-selective sets and on adaptive versus nonadaptive queries to NP

    Publication Year: 1996, Page(s):224 - 232
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (668 KB)

    We study two properties of a complexity class C-whether there exists a truth-table hard p-selective language for C, and whether polynomially-many nonadaptive queries to C can be answered by making O(log n)-many adaptive queries to C (in symbols, is PFttC⊆PFC[O(log n)]). We show that if there exists an NP-hard p-selective set under truth-table reductions, then ... View full abstract»

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  • Collapsing oracle-tape hierarchies

    Publication Year: 1996, Page(s):33 - 42
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    Other authors have shown that equipping a logspace oracle Turing machine with more than one oracle tape may result in an increased computational power. We are interested in the inverse problem: For which oracle classes C does the oracle-tape hierarchy collapse in the sense that logspace machines with a fixed number of oracle tapes cannot compute more than machines with a single oracle tape? Surpri... View full abstract»

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  • Error reduction by parallel repetition-a negative result

    Publication Year: 1996, Page(s):70 - 76
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (600 KB)

    We show that no fixed number of parallel repetitions suffices in order to reduce the error in two-prover one-round proof systems from one constant to another. Our results imply that the recent bounds proven by Ran Raz (1995), showing that the number of rounds that suffice is inversely proportional to the answer length, are nearly best possible View full abstract»

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  • Complements of multivalued functions

    Publication Year: 1996, Page(s):260 - 269
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (728 KB)

    We study the class coNPMV of complements of NPMV functions. Though defined symmetrically to NPMV this class exhibits very different properties. We clarify the complexity of coNPMV by showing that it is essentially the same as that of NPMVNP complete functions for coNPMV are exhibited and central complexity-theoretic properties of this class are studied. We show that computing maximum sa... View full abstract»

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  • L-printable sets

    Publication Year: 1996, Page(s):97 - 106
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (800 KB)

    Properties of L-printable sets are considered, and it is shown that two sets A and B that are L-printable and have similar density are L-isomorphic. L-printable sets are characterized as those sets L-isomorphic to tally sets in L, and as subsets of KS[k log n, k log n]. Several classes of L-printable sets are given, including sparse regular and context-free sets; a characterization of sparse regul... View full abstract»

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  • On the measure of two-dimensional regions with polynomial-time computable boundaries

    Publication Year: 1996, Page(s):150 - 159
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (704 KB)

    We study the computability of the Lebesgue measure of a two-dimensional region that has a polynomial-time computable boundary. It is shown that the two-dimensional measure of the boundary itself completely characterizes the computability of the measure of the interior region. Namely, if a polynomial-time computable, simple, closed curve has measure zero, then its interior region must have a comput... View full abstract»

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  • Much ado about functions

    Publication Year: 1996, Page(s):198 - 212
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (1120 KB)

    This paper surveys basic results on complexity classes of partial multivalued functions. We stress basic inclusion relations, interesting hierarchies, and results that demonstrate that hierarchies are extant View full abstract»

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  • The law of the iterated logarithm for random sequences

    Publication Year: 1996, Page(s):180 - 189
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (596 KB)

    The stochastic properties of p-random sequences are studied in this paper. It is shown that the law of the iterated logarithm holds for p-random sequences. This law gives a quantitative characterization of the density of p-random sets. When combined with the invariance property of p-random sequences, this law is also useful in proving that some complexity classes have p-measure 0 View full abstract»

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  • Good degree bounds on Nullstellensatz refutations of the induction principle

    Publication Year: 1996, Page(s):233 - 242
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (848 KB)

    This paper gives nearly optimal, logarithmic upper and lower bounds on the minimum degree of Nullstellensatz refutations (i.e., polynomials) of the propositional induction principle View full abstract»

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  • Deciding the Vapnik-Cervonenkis dimension is Σ3 p-complete

    Publication Year: 1996, Page(s):77 - 80
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (308 KB)

    Linial et al. (1988) raised the question of how difficult the computation of the Vapnik-Cervonenkis dimension of a concept class over a finite universe is. Papadimitriou and Yannakakis (1993) obtained a first answer using matrix representations of concept classes. However, this approach does not capture classes having exponential size, like monomials, which are encountered in learning theory. We c... View full abstract»

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