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Proceedings of Structure in Complexity Theory. Tenth Annual IEEE Conference

19-22 June 1995

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  • Proceedings of Structure in Complexity Theory. Tenth Annual IEEE Conference

    Publication Year: 1995
    Request permission for commercial reuse | PDF file iconPDF (186 KB)
    Freely Available from IEEE
  • Author index

    Publication Year: 1995
    Request permission for commercial reuse | PDF file iconPDF (37 KB)
    Freely Available from IEEE
  • Reductions of self-reducible sets to depth-1 weighted threshold circuit classes, and sparse sets

    Publication Year: 1995, Page(s):264 - 276
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1080 KB)

    Let LT1 denote the class of languages accepted by nonuniform families of polynomial size depth-1 circuits with a linear weighted threshold gate at the root. We show that disjunctive self-reducible bd-cylinders that many-one reduce to LT1 are in P. It follows that for C∈{NP, ModkP, PP, C=P}, if 𝒞 has a many-one hard problem in LT1 the... View full abstract»

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  • On P-immunity of nondeterministic complete sets

    Publication Year: 1995, Page(s):262 - 263
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (144 KB)

    We show that every m-complete set for NEXP as well as its complement have an infinite subset in P. This answers an open question first raised by L. Berman (1976) View full abstract»

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  • On the structure of low sets [complexity classes]

    Publication Year: 1995, Page(s):246 - 261
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1464 KB)

    Over a decade ago, V. Schoning introduced the concept of lowness into structural complexity theory. Since then a large body of results has been obtained classifying various complexity classes according to their lowness properties. In this paper we highlight some of the more recent advances on selected topics in the area. Among the lowness properties we consider are polynomial-size circuit complexi... View full abstract»

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  • Optimizing TRIEs for ordered pattern matching is Π2 P-complete

    Publication Year: 1995, Page(s):238 - 244
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (588 KB)

    We consider the complexity of constructing a data structure, called TRIEs, with the minimum operational cost for the ordered pattern matching problem, a problem abstracting the essence of executing Prolog problems; a TRIE with minimal cost corresponds to a program with the minimum worst case operational cost. Based on the recent non-approximability results developed by Arora et al. (1992) and Cond... View full abstract»

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  • Intractability of read-once resolution

    Publication Year: 1995, Page(s):29 - 36
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (600 KB)

    Read-once resolution (ROR) is a resolution proof system in which the rule (A+x)(B+x¯)→(A+B) is applied in such a way that two clauses (A+x) and (B+x¯) are replaced by (A+B), i.e., (A+x) and (B+x¯) disappear, and any clause can never be copied. Therefore ROR runs in (nondeterministic) polynomial time and is no longer complete. It is shown that, in spite of its simplicity and wea... View full abstract»

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  • A game-theoretic classification of interactive complexity classes

    Publication Year: 1995, Page(s):227 - 237
    Cited by:  Papers (5)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (884 KB)

    Game-theoretic characterisations of complexity classes have often proved useful in understanding the power and limitations of these classes. One well-known example tells us that PSPACE can be characterized by two-person, perfect-information games in which the length of a played game is polynomial in the length of the description of the initial position [by Chandra et al., see Journal of the ACM, v... View full abstract»

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  • The instance complexity conjecture

    Publication Year: 1995, Page(s):111 - 124
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (964 KB)

    This paper is concerned with instance complexity introduced by Ko, Orponen, Schoning, and Watanabe (1986) as a measure of the complexity of individual instances of a decision problem. They conjectured that for every nonrecursive r.e. set the instance complexity is infinitely often at least as high as the Kolmogorov complexity. We refute this conjecture by constructing a nonrecursive r.e. set with ... View full abstract»

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  • Weighted NP optimization problems: logical definability and approximation properties

    Publication Year: 1995, Page(s):12 - 28
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1296 KB)

    It is shown that all NP-optimization problems can be characterized by Π2 first-order formulae and that Π1 formulae are not sufficient for this goal. This generalizes the result of Kolaitis and Thakur (1990). The approximation properties of the weighted versions of MAX NP, MAX SNP, MAX SNP(π), MIN F+Π1 and MIN F+Π2(1) ... View full abstract»

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  • On approximation algorithms for hierarchical MAX-SAT

    Publication Year: 1995, Page(s):214 - 226
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (932 KB)

    We prove upper and lower bounds on performance guarantees of approximation algorithms for the hierarchical MAX-SAT (H-MAX-SAT) problem. This problem is representative of an important class of PSPACE-hard problems involving graphs, Boolean formulas and other structures that are defined “succinctly”. Our first result is that for some constant ε<1, it is PSPACE-hard to approximate... View full abstract»

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  • On finding the number of graph automorphisms

    Publication Year: 1995, Page(s):288 - 298
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (756 KB)

    This paper investigates the enumerability of the function GA, the number of automorphisms of an undirected graph, in relation to the computational complexity of GI, the Graph Isomorphism problem. A function f (on graphs) is b(n)-enumerable if there exists a function g∈PF such that for all n-node graphs G, g(G) lists b(n) numbers, one of which is f(G). The results in this paper show the follow... View full abstract»

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  • On superlinear lower bounds in complexity theory

    Publication Year: 1995, Page(s):50 - 64
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1264 KB)

    The paper first surveys the near-total lack of superlinear lower bounds in complexity theory, for “natural” computational problems with respect to many models of computation. We note that the dividing line between models where such bounds are known and those where none are known comes when the model allows non-local communication with memory at unit cost. We study a model that imposes ... View full abstract»

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  • Frequency computation and bounded queries

    Publication Year: 1995, Page(s):125 - 132
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (576 KB)

    There have been several papers over the last ten years that consider the number of queries needed to compute a function as a measure of its complexity. The following function has been studied extensively in that light: FaA(x1, …, xa)=A(x1)···A(xa). We are interested in the complexity (in terms of the numb... View full abstract»

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  • Decision trees with AND, OR queries

    Publication Year: 1995, Page(s):74 - 81
    Cited by:  Papers (2)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (736 KB)

    We investigate decision trees in which one is allowed to query threshold functions of subsets of variables. We are mainly interested in the case where only queries of AND and OR are allowed. This model is a generalization of the classical decision tree model. Its complexity (depth) is related to the parallel time that is required to compute Boolean functions in certain CRCW PRAM machines with only... View full abstract»

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  • A small span theorem for P/Poly-Turing reductions

    Publication Year: 1995, Page(s):324 - 330
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (476 KB)

    This paper investigates the structure of ESPACE under nonuniform Turing reductions that are computed by polynomial-size circuits (P/Poly-Turing reductions). A small span theorem is proven for such reductions. This result says that every language A in ESPACE satisfies at least one of the following two conditions. (i) The lower P/Poly-Turing span of A (consisting of all languages that are P/Poly-Tur... View full abstract»

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  • Resource-bounded genericity

    Publication Year: 1995, Page(s):162 - 181
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1520 KB)

    Resource-bounded genericity concepts have been introduced by Ambos-Spies, Fleischhack and Huwig (1984, 1988), Lutz (1990), and Fenner (1991). Though it was known that these concepts are incompatible, the relations among these notions were not fully understood. We survey these notions and clarify the relations among them by specifying the types of diagonalizations captured by the individual concept... View full abstract»

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  • Inverting the Turing jump in complexity theory

    Publication Year: 1995, Page(s):102 - 110
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (612 KB)

    The paper investigates the invertibility of certain analogs of the Turing jump operator in the polynomial-time Turing degrees. If 𝒞 is some complexity class, the 𝒞-jump of a set A is the canonical 𝒞-complete set relative to A. It is shown that the PSPACE-jump and EXP-jump operators are not invertible, i.e., there is a PSPACE-hard (resp. EXP-hard) set that is not p-time Turing equiva... View full abstract»

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  • Counting quantifiers, successor relations, and logarithmic space

    Publication Year: 1995, Page(s):2 - 11
    Cited by:  Papers (8)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (628 KB)

    We present new expressibility lower bounds for a logic with a weak form of ordering using model theoretic games. Our lower bound is on first-order logic augmented with counting quantifiers, a logical language that over structures with a total-ordering has exactly the power of the class TC0. We prove that it cannot express a property ORD in L, over structures with a successor relation. T... View full abstract»

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  • Restricted information from nonadaptive queries to NP

    Publication Year: 1995, Page(s):206 - 213
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (540 KB)

    We investigate classes of sets that can be decided by bounded truth-table reductions to an NP set in which evaluators do not have full access to the answers to the queries but get only restricted information such as the number of queries that are in the oracle set or even just this number modulo m, for some m⩾2. We also investigate the case in which evaluators are nondeterministic. We locate a... View full abstract»

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  • The power of local self-reductions

    Publication Year: 1995, Page(s):277 - 285
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (596 KB)

    Identify a string x over {0, 1} with the positive integer whose binary representation is 1x. We say that a self-reduction is k-local if on input x all queries belong to {x-1, …, x-k}. We show that all k-locally self-reducible sets belong to PSPACE. However, the power of k-local self-reductions changes drastically between k=2 and k=3. Although all 2-locally self-reducible sets belong to MOD<... View full abstract»

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  • Semantics versus syntax versus computations. Machine models for type-2 polynomial-time bounded functionals

    Publication Year: 1995, Page(s):37 - 48
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (984 KB)

    The paper investigates analogs of the Kreisel-Lacombe-Shoenfield (1957) Theorem in the context of the type-2 basic feasible functionals, aka the Mehlhorn-Cook class of type-2 polynomial-time functionals. We develop a direct, polynomial-time analog of effective operation, where the time bound on computations is modeled after Kapron and Cook's (1990) scheme for their basic polynomial-time functional... View full abstract»

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  • On the power of number-theoretic operations with respect to counting

    Publication Year: 1995, Page(s):299 - 314
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1176 KB)

    We investigate function classes ⟨P⟩f which are defined as the closure of P under the operation f and a set of known closure properties of P, e.g. summation over an exponential range. First, we examine operations f under which P is closed (i.e., ⟨P⟩f=P) in every relativization. We obtain the following complete characterization of these operations: P is clos... View full abstract»

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  • Fault tolerant circuits and probabilistically checkable proofs

    Publication Year: 1995, Page(s):65 - 73
    Cited by:  Papers (4)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (704 KB)

    We introduce a new model of fault tolerance for Boolean circuits. We consider synchronized circuits and we allow an adversary to choose a small constant fraction of the gates at each level of the circuit to be faulty. We require that even in the presence of such faults the circuit compute a “loose version” of the given function. We show that every symmetric function has a small (size O... View full abstract»

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  • A personal view of average-case complexity

    Publication Year: 1995, Page(s):134 - 147
    Cited by:  Papers (29)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (924 KB)

    The structural theory of average-case complexity, introduced by Levin (1986), gives a formal setting for discussing the types of inputs for which a problem is difficult. This is vital to understanding both when a seemingly difficult (e.g. NP-complete) problem is actually easy on almost all instances, and to determining which problems might be suitable for applications requiring hard problems, such... View full abstract»

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