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[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
  • Proceedings of 1993 IEEE 8th Annual Conference on Structure in Complexity Theory

    Publication Year: 1993
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    Freely Available from IEEE
  • Pointers versus arithmetic in PRAMs

    Publication Year: 1993, Page(s):239 - 252
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1024 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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  • On span programs

    Publication Year: 1993, Page(s):102 - 111
    Cited by:  Papers (58)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (776 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 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 (564 KB)

    The computational power of the counting class ModP, which generalizes the classes ModpP, 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... 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 (22)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (528 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 (k) of the magnitude of these problems to withi... 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 (880 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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  • On monadic NP vs. monadic co-NP

    Publication Year: 1993, Page(s):19 - 30
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (964 KB)

    It is proved that connectivity of finite graphs is not in monadic NP, even in the presence of arbitrary built-in relations of moderate degree (that is, degree (log n) o(1)). This results in a strong separation between monadic NP and monadic co-NP. The proof uses a combination of three techniques: (1) a technique of W. Hanf (1965) for showing that two (infinite) structures agree... 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 (456 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 NPA-sets that are separable by no PA-set, (2) there is a pair of disjoint Co-NPA-sets that are separable by no PA-set, and (3) there is an infinite Co-NPA-set having no infinite NPA 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 (496 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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  • The quantitative structure of exponential time

    Publication Year: 1993, Page(s):158 - 175
    Cited by:  Papers (8)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1084 KB)

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

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  • 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 (952 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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  • SPARSE reduces conjunctively to TALLY

    Publication Year: 1993, Page(s):208 - 214
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (480 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 View full abstract»

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  • Alternating time versus deterministic time: a separation

    Publication Year: 1993, Page(s):266 - 277
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    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 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 (420 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(2linear ) and EXP-DTIME(2poly) are shown View full abstract»

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  • Polynomial-time optimization, parallel approximation, and fixpoint logic

    Publication Year: 1993, Page(s):31 - 41
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (860 KB)

    A study of polynomial-time optimization from the perspective of descriptive complexity theory is initiated. It is established that the class of polynomial-time and polynomially bounded optimization problems with ordered finite structures as instances can be characterized in terms of the stage functions of positive first-order formulas, i.e., the functions that compute the number of distinct stages... 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 (1160 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 View full abstract»

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  • Lower bounds on representing Boolean functions as polynomials in Zm

    Publication Year: 1993, Page(s):96 - 101
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (352 KB)

    The MODm-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 MODm-de... View full abstract»

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  • On closure properties of #P in the context of PF {omicron} #P

    Publication Year: 1993, Page(s):139 - 146
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (568 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 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 (756 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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  • On limited nondeterminism and the complexity of the V-C dimension

    Publication Year: 1993, Page(s):12 - 18
    Cited by:  Papers (13)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (548 KB)

    The complexity of several natural computational problems in NP, which have been proposed but not categorized satisfactorily in the literature is characterized precisely. These problems can be solved in nO(logn) time, and thus they are probably not NP-complete. Two new complexity classes between P and NP, very much in the spirit of MAXNP and MAXSNP, are defined. It is shown that... 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 (896 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 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 (14)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (524 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~ reject, 1~ 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... View full abstract»

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  • On completeness under random reductions

    Publication Year: 1993, Page(s):176 - 184
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    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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  • Relativized limitations of left set technique and closure classes of sparse sets

    Publication Year: 1993, Page(s):215 - 222
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (604 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 View full abstract»

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  • The polynomial method in circuit complexity

    Publication Year: 1993, Page(s):82 - 95
    Cited by:  Papers (29)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (936 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 View full abstract»

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