[1993] Proceedings of the Eigth Annual Structure in Complexity Theory Conference

18-21 May 1993

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Displaying Results 1 - 25 of 32
  • The complexity of selecting maximal solutions

    Publication Year: 1993, Page(s):313 - 325
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1121 KB)

    Specific maximization problems, such as the maximal independent set problem and the minimal unsatisfiability problem, are studied in a general framework. The goal is to show what factors make maximization problems hard or easy to solve and how the factors influence the complexity of solving the problems. Maximization problems are divided into several classes, and both upper and lower bounds for th... View full abstract»

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  • NP-complete problems have a version that's hard to approximate

    Publication Year: 1993, Page(s):305 - 312
    Cited by:  Papers (25)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (626 KB)

    It is proved that all of R.M. Karp's (1972) 21 original NP-complete problems have a version that is hard to approximate. These versions are obtained from the original problems by adding essentially the same, simple constraint. It is further shown that these problems are absurdly hard to approximate. In fact, one cannot even approximate log/sup (k)/ of the magnitude of these problems to within a co... View full abstract»

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  • Taking it to the limit: on infinite variants of NP-complete problems

    Publication Year: 1993, Page(s):292 - 304
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (904 KB)

    Infinite, recursive versions of NP optimization problems are defined. For example, MAX CLIQUE becomes the question of whether a recursive graph contains an infinite clique. The work was motivated by trying to understand what makes some NP problems highly undecidable in the infinite case, while others remain on low levels of the arithmetical hierarchy. Two results are proved; one enables using know... View full abstract»

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  • Computing functions with parallel queries to NP

    Publication Year: 1993, Page(s):280 - 291
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1148 KB)

    The characterizations of the class Theta /sub 2//sup p/ of languages polynomial-time truth-table reducible to sets in NP are surveyed studying the classes obtained when the characterizations are used to define functions instead of languages. It is shown that in this way three function classes are obtained. An overview of the known relationships between these classes, including some original result... View full abstract»

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  • Alternating time versus deterministic time: a separation

    Publication Year: 1993, Page(s):266 - 277
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1246 KB)

    It is shown that only two alternations are sufficient to achieve a log*t(n) speed-up of deterministic Turing machines. Using this speed-up it is shown that for each time-constructible function t(n), two alternations are strictly more powerful than deterministic time.<<ETX>> View full abstract»

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  • Some structural complexity aspects of neural computation

    Publication Year: 1993, Page(s):253 - 265
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1033 KB)

    Recent work by H.T. Siegelmann and E.D. Sontag (1992) has demonstrated that polynomial time on linear saturated recurrent neural networks equals polynomial time on standard computational models: Turing machines if the weights of the net are rationals, and nonuniform circuits if the weights are real. Here, further connections between the languages recognized by such neural nets and other complexity... View full abstract»

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  • Pointers versus arithmetic in PRAMs

    Publication Year: 1993, Page(s):239 - 252
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1197 KB)

    A parallel pointer machine, (PPM) is a parallel model having pointers as its principal data type. PPMs have been characterized as PRAMs obeying two restrictions: restricted arithmetic capabilities and the CROW (concurrent read, owner write) memory access restriction. Results concerning the relative power of PPMs (and other arithmetically restricted PRAMs) versus CROW PRAMs having ordinary arithmet... View full abstract»

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  • Complexity and structure in formal language theory

    Publication Year: 1993, Page(s):224 - 238
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1328 KB)

    Some connections between formal languages and complexity are reviewed. Families of formal languages are treated with complexity theoretical methods. In particular, the concept of unambiguity, common to both areas, is treated in detail. Some new results on deterministic families of formal languages and on complexities of operations on formal languages are indicated.<<ETX>> View full abstract»

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  • Relativized limitations of left set technique and closure classes of sparse sets

    Publication Year: 1993, Page(s):215 - 222
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (711 KB)

    A number of theorems are proved by introducing the notion of k-families of sets of strings, and an algorithm which outputs the sets of certain k-families is given. The algorithm is used to disjunctively reduce the left set (or 1wdsr set) to a sparse set. The set output by the algorithm on an input corresponds to the set queried by the disjunctive reduction on the input.<<ETX>> View full abstract»

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  • SPARSE reduces conjunctively to TALLY

    Publication Year: 1993, Page(s):208 - 214
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (572 KB)

    Polynomials over finite fields are used to conjunctively reduce any sparse set to a tally set. This leads to the derivation of new results and to new simple proofs of known results about various classes that lie between P and P/poly.<<ETX>> View full abstract»

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  • On the power of polynomial time bit-reductions

    Publication Year: 1993, Page(s):200 - 207
    Cited by:  Papers (15)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (614 KB)

    For a nondeterministic polynomial-time Turing machine M and an input string x, the leaf string of M on x is the 0-1-sequence of leaf-values (0 approximately reject, 1 approximately accept) of the computation tree of M with input x. The set A is said to be bit-reducible to B if there exists and M as above such that every input x is in A if and only if the leaf string of M on x is in B. A class C is... View full abstract»

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  • Sperner's lemma and robust machines

    Publication Year: 1993, Page(s):194 - 199
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (357 KB)

    Sperner's lemma states that any admissible coloring of any triangulation of the unit triangle has a three-colored triangle. It is shown that any algorithm to find a three-colored triangle in any admissible coloring that treats the coloring itself as an oracle must be in the worst case linear in n. By making use of such lower bound, a negative answer is obtained for two problems regarding robust or... View full abstract»

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  • With quasi-linear queries, EXP is not polynomial time Turing reducible to sparse sets

    Publication Year: 1993, Page(s):185 - 191
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (513 KB)

    The lower bounds of queries required by the polynomial-time Turing reductions from exponential time classes to the sets of small density are investigated. Results for complexity classes E=DTIME(2/sup linear/) and EXP-DTIME(2/sup poly/) are shown.<<ETX>> View full abstract»

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  • On completeness under random reductions

    Publication Year: 1993, Page(s):176 - 184
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (853 KB)

    The authors study the notion of completeness under random reductions and explore how that depends on the type and success probability of the reduction. They obtain absolute separations between completeness notions under various random reductions and between random reductions and deterministic reductions. These separations are obtained in appropriately high complexity classes where these questions ... View full abstract»

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  • The quantitative structure of exponential time

    Publication Year: 1993, Page(s):158 - 175
    Cited by:  Papers (10)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1273 KB)

    Recent results on the internal, measure-theoretic structure of the exponential time complexity classes E=DTIME(2/sup linear/) and E/sub 2/=DTIME(2/sup polynomial/) are surveyed. The measure structure of these classes is seen to interact in informative ways with bi-immunity, complexity cores, /sub <or=/m/sup P/-reducibility, circuit-size complexity, Kolmogorov complexity, and the density of hard... View full abstract»

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  • On the power of generalized MOD-classes

    Publication Year: 1993, Page(s):147 - 155
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (670 KB)

    The computational power of the counting class ModP, which generalizes the classes Mod/sub p/P, p prime, is investigated. It is shown that ModP is truth-table equivalent in power to MP, and that ModP is contained in the class AmpMP. As a consequence, the lowness of AmpMP or of ModP for MP would imply the collapse of the counting hierarchy (CH) to MP. Further, every set in C=P is shown to be reducib... View full abstract»

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  • On closure properties of Hash P in the context of PF (omicron) Hash P

    Publication Year: 1993, Page(s):139 - 146
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (686 KB)

    It is shown that while absolute answers to open questions about relationships between counting classes seem hard to get, it is still possible to obtain relative answers that help us to develop intuition about or understanding of these relationships. In particular, a structural approach to extending such understanding is proposed.<<ETX>> View full abstract»

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  • Relationships between NP-sets, Co-NP-sets, and P-sets relative to random oracles

    Publication Year: 1993, Page(s):132 - 138
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (559 KB)

    It is proved that relative to random oracle A (with respect to the uniform measure) the following assertions hold: (1) there is a pair of disjoint NP/sup A/-sets that are separable by no P/sup A/-set, (2) there is a pair of disjoint Co-NP/sup A/-sets that are separable by no P/sup A/-set, and (3) there is an infinite Co-NP/sup A/-set having no infinite NP/sup A/-subset.<<ETX>> View full abstract»

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  • On oracle builder's toolkit

    Publication Year: 1993, Page(s):120 - 131
    Cited by:  Papers (13)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1063 KB)

    It is shown how to use various notions of genericity as a tool in oracle creation. A general framework for defining different types of generic sets in terms of arithmetic forcing is given. A number of basic facts about Cohen generic sets, many of which are generalizations of known results, are systematically assembled. We define sp-generic sets and extend some previous results.<<ETX>> View full abstract»

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  • On proving lower bounds for circuit size

    Publication Year: 1993, Page(s):112 - 118
    Cited by:  Papers (7)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (597 KB)

    A.A. Razborov's (1989) generalized approximation method, which has the potential of giving tight lower bounds for circuit size, is considered. The method is described in a more intuitive fashion, and its analogy with the ultraproduct construction in model theory is made explicit. The method is extended so that it can be used to lower bound nondeterministic circuit size. Using the proposed framewor... View full abstract»

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  • On span programs

    Publication Year: 1993, Page(s):102 - 111
    Cited by:  Papers (88)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (929 KB)

    A linear algebraic model of computation the span program, is introduced, and several upper and lower bounds on it are proved. These results yield applications in complexity and cryptography. The proof of the main connection, between span programs and counting branching programs, uses a variant of Razborov's general approximation method.<<ETX>> View full abstract»

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  • Lower bounds on representing Boolean functions as polynomials in Z/sub m/

    Publication Year: 1993, Page(s):96 - 101
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (424 KB)

    The MOD/sub m/-degree of Boolean function F is defined to be the smallest degree of any polynomial P, over the ring of integers modulo m, such that for all 0-1 assignments x, F(x)=0 iff P(x)=0. By exploring the periodic property of the binomial coefficients module m, two new lower bounds on the MOD/sub m/-degree of the MOD/sub l/ and not-MOD/sub m/ functions are proved, where m is any composite in... View full abstract»

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  • The polynomial method in circuit complexity

    Publication Year: 1993, Page(s):82 - 95
    Cited by:  Papers (31)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1107 KB)

    The basic techniques for using polynomials in complexity theory are examined, emphasizing intuition at the expense of formality. The focus is on the connections to constant-depth circuits, at the expense of polynomial-time Turing machines. The closure properties, upper bounds, and lower bounds obtained by this approach are surveyed.<<ETX>> View full abstract»

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  • Polynomial isomorphism of 1-L-complete sets

    Publication Year: 1993, Page(s):75 - 80
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (502 KB)

    Let C be any complexity class closed under log-lin reductions. It is shown that all complete sets for C under 1-L reductions are polynomial time isomorphic to one other. It is indicated how to generalize the result to reductions computed by finite-crossing machines.<<ETX>> View full abstract»

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  • Isomorphisms of NP complete problems on random instances

    Publication Year: 1993, Page(s):65 - 74
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (811 KB)

    Polynomial isomorphisms are defined for NP-complete sets on random instances. Not only are polynomial-time computable and invertible bijections among complete sets considered, but also it is required that these bijections preserve distributions on random instances of these sets. Sufficient conditions for randomized decision problems to be polynomially isomorphic are shown. It is then proved that a... View full abstract»

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