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

18-21 May 1993

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

    Publication Year: 1993
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    Freely Available from IEEE
  • 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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  • Polynomial-time optimization, parallel approximation, and fixpoint logic

    Publication Year: 1993, Page(s):31 - 41
    Cited by:  Papers (1)
    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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  • P-selective self-reducibles sets: a new characterization of P

    Publication Year: 1993, Page(s):44 - 51
    Cited by:  Papers (8)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (624 KB)

    It is shown that any p-selective and self-reducible sets is in P. As the converse is also true, the authors obtain a new characterization of the class P. A generalization and several consequences of this theorem are discussed. Among other consequences, it is shown that under reasonable assumptions autoreducibility and self-reducibility differ on NP, and there are non-p-T-mitotic sets in NP 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 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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  • 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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  • P-selective sets, and reducing search to decision vs. self-reducibility

    Publication Year: 1993, Page(s):52 - 64
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (836 KB)

    Several results that distinguish self-reducibility of a language L with the question of whether search reduces to decision for L are obtained. It is proved that if NE∩co-NE≠E, then there exists a set L in NP-P such that search reduces to decision for L, search does not nonadaptively reduce to decision for L, and L is not self-reducible. ... View full abstract»

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  • Towards uncheatable benchmarks

    Publication Year: 1993, Page(s):2 - 11
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (656 KB)

    The problem of how to make benchmarks resistant to tampering and hence more trustworthy is studied. Some schemes that are based on modern cryptography and complexity theory are proposed to make benchmarks uncheatable. The philosophy is the same as that of encryption-decryption schemes, namely, that trust in individuals and organizations is replaced by trust in the impossibility of breaking certain... 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 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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  • 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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  • 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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  • 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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  • 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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  • 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 (688 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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  • Computing functions with parallel queries to NP

    Publication Year: 1993, Page(s):280 - 291
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (976 KB)

    The characterizations of the class Θ2p 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 orig... View full abstract»

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  • The polynomial method in circuit complexity

    Publication Year: 1993, Page(s):82 - 95
    Cited by:  Papers (30)
    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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  • 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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  • 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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  • 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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  • 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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  • 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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  • 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 (296 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 ... 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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