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[1992] Proceedings of the Seventh Annual Structure in Complexity Theory Conference

22-25 June 1992

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Displaying Results 1 - 25 of 35
  • Proceedings of the Seventh Annual Structure in Complexity Theory Conference (Cat. No.92CH3167-4)

    Publication Year: 1992
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    Freely Available from IEEE
  • Fixed-parameter intractability

    Publication Year: 1992, Page(s):36 - 49
    Cited by:  Papers (12)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1268 KB)

    The authors consider the complexity behavior of parametrized problems that they term fixed-parameter tractability: for each fixed parameter value y the problem is solvable in time O( nc), where c is a constant independent of the parameter y. They introduce a structure theory with which to address the apparent intractability of some parameteri... View full abstract»

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  • On the power of PP

    Publication Year: 1992, Page(s):138 - 143
    Cited by:  Papers (5)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (384 KB)

    It is proved that MA is a subset of PP (relativizable) and that the intersection of AMA and co-AMA is not a subset of PPA for some oracle A View full abstract»

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  • A sublinear space, polynomial time algorithm for directed s-t connectivity

    Publication Year: 1992, Page(s):27 - 33
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (468 KB)

    A deterministic sublinear space, polynomial-time algorithm for directed s-t connectivity, which is the problem of detecting whether there is a path from vertex s to vertex t in a directed graph, is presented. For n-vertex graphs, the algorithm can use as little as n/2Θ(√log n) space while still running in polyno... View full abstract»

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  • The quantum challenge to structural complexity theory

    Publication Year: 1992, Page(s):132 - 137
    Cited by:  Papers (9)  |  Patents (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (456 KB)

    A nontechnical survey of recent quantum-mechanical discoveries that challenge generally accepted complexity-theoretic versions of the Church-Turing thesis is presented. In particular, the authors construct an oracle relative to which there exists a set that can be recognized in quantum polynomal time (QP), yet any Turing machine that recognizes it would require exponential time even if allowed to ... View full abstract»

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  • The power of negative thinking in constructing threshold circuits for addition

    Publication Year: 1992, Page(s):20 - 26
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (544 KB)

    It has recently been shown that it is possible to add two binary numbers in threshold circuits of depth two with polynomial size. It is shown here that the most significant bit of addition, which is a monotone function, needs exponential size when computed in monotone threshold circuits of depth two. In fact, it is shown that even o (n/log n) negations do not suffice for... View full abstract»

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  • Interactive proof systems with polynomially bounded strategies

    Publication Year: 1992, Page(s):282 - 294
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1020 KB)

    Interactive proof systems in which the prover is restricted to have a polynomial size strategy are investigated. The restriction of polynomial-size computation tree, or logarithmically bounded number of coin flips, guarantees a polynomial-size strategy. One result is that interactive proof systems in which the prover is restricted to a polynomial-size strategy are equivalent to MA, Merlin-Arthur g... View full abstract»

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  • On the nonuniform complexity of the graph isomorphism problem

    Publication Year: 1992, Page(s):118 - 129
    Cited by:  Papers (8)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (872 KB)

    The nonuniform complexity of the graph isomorphism (GI) and graph automorphism (GA) problems is studied, and the implications of different types of polynomial-time reducibilities from these problems to sparse sets are considered. It is shown that if GI (or GA) is bounded truth-table or conjunctively reducible to a sparse set, then it is in P; if it is supposed that it is truth-table reducible with... View full abstract»

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  • On average P vs. average NP

    Publication Year: 1992, Page(s):318 - 326
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (688 KB)

    Structures of polynomial-time computable distributions and polynomial-time many-one reductions on randomized decision problems are investigated. The scope is widened from the most studied class DNP (distributional-NP) to the class ANP (average-NP), which consists of randomized decision problems accepted by nondeterministic Turing machines in average polynomial time. Results indicate that the struc... View full abstract»

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  • Perceptrons, PP, and the polynomial hierarchy

    Publication Year: 1992, Page(s):14 - 19
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (364 KB)

    The author constructs a predicate that is computable by a perceptron with linear size, order one, and exponential weights, but which cannot be computed by any perceptron having subexponential size, subpolynomial order, and subexponential weights. A consequence is that there is an oracle relative to which PNP is not contained in PP View full abstract»

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  • Non-deterministic communication complexity with few witnesses

    Publication Year: 1992, Page(s):275 - 281
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (464 KB)

    Nondeterministic communication protocols in which no input has too many witnesses are studied. Two different lower bounds are presented for nk(f), defined as the minimum complexity of a nondeterministic protocol for the function f in which each input has at most k witnesses. One result shows that n k(f) is bounded below by... View full abstract»

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  • The power of the middle bit

    Publication Year: 1992, Page(s):111 - 117
    Cited by:  Papers (5)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (452 KB)

    The class of languages that can be recognized in polynomial time with the additional information of one bit from a P function is studied. In particular, it is shown that every ModkP class and every class contained in PH are low for this class. These results are translated to the area of circuit complexity using MidBit (middle bit) gates. It is shown that every language in ACC c... View full abstract»

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  • Average dependence and random oracles

    Publication Year: 1992, Page(s):306 - 317
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (840 KB)

    A reconstruction of the foundations of complexity theory relative to random oracles is begun. The goals are to identify the simple, core mathematical principles behind randomness; to use these principles to push hard on the current boundaries of randomness; and to eventually apply these principles in unrelativized complexity. The focus in this work is on quantifying the degree of separation betwee... View full abstract»

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  • The power of adaptiveness and additional queries in random-self-reductions

    Publication Year: 1992, Page(s):338 - 346
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (656 KB)

    Relationships between adaptive and nonadaptive random-self-reductions are examined. The question of what happens to random-self-reductions if the number of queries they are allowed to make is restricted is also explored. The following results are shown. (1) There exist sets that are adaptively random-self-reducible but not nonadaptively random-self-reducible. Under reasonable assumptions, there ex... View full abstract»

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  • Majority gates vs. general weighted threshold gates

    Publication Year: 1992, Page(s):2 - 13
    Cited by:  Papers (9)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (784 KB)

    Small-depth circuits that contain threshold gates (with or without weights) and parity gates are studied. All circuits considered are of polynomial size. Several results that complete the work of characterizing possible inclusions between many classes defined by small-depth circuits are proved View full abstract»

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  • On randomized reductions to sparse sets

    Publication Year: 1992, Page(s):239 - 242
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (276 KB)

    It is shown that the existence of a sparse set that is hard for the class NP under certain randomized reductions implies that NP=RP and hence all languages in the polynomial-time hierarchy can be recognized feasibly. This provides strong evidence for the nonexistence of such sets View full abstract»

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  • Fractional covers and communication complexity

    Publication Year: 1992, Page(s):262 - 274
    Cited by:  Papers (5)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (944 KB)

    It is possible to view communication complexity as the solution of an integer programming problem. The authors relax this integer programming problem to a linear programming problem, and try to deduce from it information regarding the original communication complexity question. This approach works well for nondeterministic communication complexity. In this case the authors get a special case of Lo... View full abstract»

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  • Functional characterizations of uniform log-depth and polylog-depth circuit families

    Publication Year: 1992, Page(s):193 - 206
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (936 KB)

    The classes of functions computable by uniform log-depth (NC1 ) and polylog-depth circuit families are characterized as closures of a set of base functions. (The former is equivalent to ALOGTIME, the latter to polylogarithmic space.) The closures involve the `safe' composition of S. Bellantoni and S. Cook (1992) as well as a safe divide-and-conquer recursion: a simple change to the defi... View full abstract»

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  • Self-witnessing polynomial-time complexity and prime factorization

    Publication Year: 1992, Page(s):107 - 110
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (300 KB)

    For a number of computational search, problems, the existence of a polynomial-time algorithm for the problem implies that such an algorithm for the problem is constructively known. Some instances of such self-witnessing polynomial-time complexity are presented. The main result demonstrates this property for the problem of computing the prime factorization of a positive integer, based on a lemma wh... View full abstract»

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  • Some properties of exponential time complexity classes

    Publication Year: 1992, Page(s):50 - 57
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (476 KB)

    The authors separate NE from Px (NP), where x= n0(1)-T. The class EXP-low[1] is introduced and applied in the investigations of stable properties for both EXP and NEXP hard sets. A set A is in EXP-low[1](EXP-low resp.) if EXP A[1]=EXP(EXPA=EXP). The authors separate EXP-low[1] from EXP-low by constructing a set A View full abstract»

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  • Formal power series: an algebraic approach to the GapP and #P functions

    Publication Year: 1992, Page(s):144 - 154
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (628 KB)

    The algebraic structure of GapP and #P functions is introduced by formalizing them as power series ring and semiring, respectively. It is proved that for every invertible GapP function g, Pg=P1g/, and for all positive integers i, Pg=P to the gi, power. Applying the Ladner theorem for functions, it is shown that Ps=P<... View full abstract»

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  • Some lower and upper bounds for algebraic decision trees and the separation problem

    Publication Year: 1992, Page(s):295 - 304
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (484 KB)

    The complexity of computing Boolean functions with algebraic decision trees over GF(2) and R is considered. Some lower and upper bounds for algebraic decision trees of various degrees are found. It is shown that over GF(2) decision trees of degree d are more powerful than trees of degree <d. For the case of decision trees over R, it is shown that decision trees of degree ⩾... View full abstract»

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  • A note on the instance complexity of pseudorandom sets

    Publication Year: 1992
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (780 KB)

    The relationship between the notion of pseudorandomness and the notion of hard instances is investigated. It is proved that if A is random (or pseudorandom), then most instances to A are hard instances (or, respectively, have nontrivial instance complexity). These results are used to show that if one-way functions that are secure against polynomial-size circuits exist, then an NP... View full abstract»

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  • On closeness of NP-hard sets to other complexity classes

    Publication Year: 1992, Page(s):243 - 248
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (356 KB)

    The difference between NP and other complexity classes is examined. The question of whether an NP-hard set can be approximated sufficiently by the sets in other complexity classes is studied View full abstract»

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  • Universal relations

    Publication Year: 1992, Page(s):207 - 220
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (936 KB)

    Two operators, join and equivalence, are defined on R, a polynomial-time verifiable binary relation witnessing language A in NP. It is proved that if R has these two operators and there is an instance of A with certain specific properties, then A is NP-complete. Relations with the above properties are called universal relations. It is shown that if set ... View full abstract»

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