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
  • Counting quantifiers, successor relations, and logarithmic space

    Publication Year: 1995, Page(s):2 - 11
    Cited by:  Papers (9)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (756 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 TC/sup 0/. We prove that it cannot express a property ORD in L, over structures with a successor relation. This h... 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 (1547 KB)

    It is shown that all NP-optimization problems can be characterized by /spl Pi//sub 2/ first-order formulae and that /spl Pi//sub 1/ 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(/spl pi/), MIN F/sup +//spl Pi//sub 1/ and MIN F/sup +//spl Pi//sub 2/(1) are analyz... View full abstract»

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  • Intractability of read-once resolution

    Publication Year: 1995, Page(s):29 - 36
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (724 KB)

    Read-once resolution (ROR) is a resolution proof system in which the rule (A+x)(B+. 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 (1170 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 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 (1526 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 a "fair cost... 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 (824 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(n), depth O... View full abstract»

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  • Decision trees with AND, OR queries

    Publication Year: 1995, Page(s):74 - 81
    Cited by:  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (875 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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  • Semi-unbounded fan-in circuits: Boolean vs. arithmetic

    Publication Year: 1995, Page(s):82 - 87
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (496 KB)

    We prove that polynomial size semi-unbounded fan-in Boolean circuits of depth d can be simulated by polynomial size semi-unbounded fan-in arithmetic circuits of depth O(d+log n), where the arithmetic operations +, -, /spl times/ are performed in an arbitrary finite field. It is impossible to achieve this via gate-by-gate simulation. Instead, the proof is based on a randomized reduction to "unique ... View full abstract»

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  • The isomorphism conjecture holds and one-way functions exist relative to an oracle

    Publication Year: 1995, Page(s):90 - 101
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (980 KB)

    We demonstrate an oracle relative to which there are one-way functions but every paddable 1-li-degree collapses to an isomorphism type, thus yielding a relativized failure of the Joseph-Young (1985) conjecture (JYC). We then use this result to construct an oracle relative to which the isomorphism conjecture (IC) is true but one-way functions exist, which answers an open question of Fenner, Fortnow... 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 (736 KB)

    The paper investigates the invertibility of certain analogs of the Turing jump operator in the polynomial-time Turing degrees. If /spl Cscr/ is some complexity class, the /spl Cscr/-jump of a set A is the canonical /spl Cscr/-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 T... 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 (1152 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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  • Frequency computation and bounded queries

    Publication Year: 1995, Page(s):125 - 132
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (699 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: F/sub a//sup A/(x/sub 1/, ..., x/sub a/)=A(x/sub 1/)/spl middot//spl middot//spl middot/A(x/sub a/). We are interested in the complexity (in terms of the number of queries) of appro... View full abstract»

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  • A personal view of average-case complexity

    Publication Year: 1995, Page(s):134 - 147
    Cited by:  Papers (41)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1070 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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  • Towards average-case complexity analysis of NP optimization problems

    Publication Year: 1995, Page(s):148 - 159
    Cited by:  Papers (2)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (995 KB)

    For the worst-case complexity measure, if P=NP, then P=OptP, i.e., all NP optimization problems are polynomial-time solvable. On the other hand, it is not clear whether a similar relation holds when considering average-case complexity. We investigate the relationship between the complexity of NP decision problems and that of NP optimization problems under polynomial-time computable distributions, ... View full abstract»

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  • Resource-bounded genericity

    Publication Year: 1995, Page(s):162 - 181
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1761 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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  • Resource-bounded Baire category: a stronger approach

    Publication Year: 1995, Page(s):182 - 192
    Cited by:  Papers (5)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (979 KB)

    The paper introduces a new definition of resource-bounded Baire category in the style of Lutz (1987, 1990, 1992) . This definition gives an almost-all/almost-none theory of various complexity classes. The meagerness/comeagerness of many more classes can be resolved in the new definition than in previous definitions. For example, almost no sets in EXP are EXP-complete, and NP is PF-meager unless NP... View full abstract»

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  • A note on genericity and bi-immunity

    Publication Year: 1995, Page(s):193 - 196
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (403 KB)

    Generic sets have all properties (from among a suitably chosen class) that can be enforced by finite extension arguments. In particular, p-generic sets known to be P-bi-immune. We try to clarify the precise relationship between genericity and bi-immunity by proposing an extended notion of bi-immunity that exactly characterizes the p-generic sets. View full abstract»

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  • An excursion to the Kolmogorov random strings

    Publication Year: 1995, Page(s):197 - 203
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (631 KB)

    We study the set of resource bounded Kolmogorov random strings: R/sub 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 (647 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/spl ges/2. We also investigate the case in which evaluators are nondeterministic. We loca... View full abstract»

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  • On approximation algorithms for hierarchical MAX-SAT

    Publication Year: 1995, Page(s):214 - 226
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1107 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 /spl epsiv/<1, it is PSPACE-hard to approximate the fu... 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 (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1051 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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  • Optimizing TRIEs for ordered pattern matching is /spl Pi//sub 2//sup P/-complete

    Publication Year: 1995, Page(s):238 - 244
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (710 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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  • 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 (1736 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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  • 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 (182 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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