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

22-25 June 1992

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  • 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 (14)
    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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  • A sublinear space, polynomial time algorithm for directed s-t connectivity

    Publication Year: 1992, Page(s):27 - 33
    Cited by:  Papers (5)
    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 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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  • 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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  • 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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  • 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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  • 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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  • Descriptive complexity of #P functions

    Publication Year: 1992, Page(s):169 - 184
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1108 KB)

    A logic-based framework for defining counting problems is given, and it is shown that it exactly captures the problems in Valiant's counting class #P. The expressive power of the framework is studied under natural syntactic restrictions, and it is shown that some of the subclasses obtained in this way contain problems in #P with interesting computational properties. In particular, using syntactic ... View full abstract»

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  • On languages with very high information content

    Publication Year: 1992, Page(s):255 - 259
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (364 KB)

    It is shown that any language in ESPACE that is bounded truth-table reducible in polynomial time to a set with very high space-bounded Kolmogorov complexity must be bounded truth-table reducible in polynomial time to a sparse set View full abstract»

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  • Saving queries with randomness

    Publication Year: 1992, Page(s):71 - 83
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (896 KB)

    The power of randomness to save a query to an NP-complete set is studied. Error probabilities for the random reduction of the P SAT||[k]⩽mP-complete language to a language in PSAT||[k-1] are obtained. It is proved that these probability bounds are tight unless PH collapses. Tight performance bounds on several randomized r... View full abstract»

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  • Universal relations

    Publication Year: 1992, Page(s):207 - 220
    Cited by:  Papers (2)
    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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  • On closeness of NP-hard sets to other complexity classes

    Publication Year: 1992, Page(s):243 - 248
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    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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  • 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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  • 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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  • 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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  • 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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  • Fixpoint logics, relational machines, and computational complexity

    Publication Year: 1992, Page(s):156 - 168
    Cited by:  Papers (8)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1016 KB)

    To overcome the inherent mismatch between complexity and logic, i.e., that while computational devices work on encodings of problems, logic is applied directly to the underlying mathematical structures, the authors develop a theory of relational complexity that bridges the gap between standard complexity and fixpoint logic. It is shown that questions about containments among standard complexity cl... 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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  • A purely logical characterization of circuit uniformity

    Publication Year: 1992, Page(s):185 - 192
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (596 KB)

    Utilizing the connection between uniform constant-depth circuits and first-order logic with numerical predicates, the author provides a purely logical characterization of uniformity based on the intrinsic properties of these predicates. By requiring a numerical predicate R to satisfy a natural extensibility condition-that it can be translated to a polynomially magnified domain based on t... 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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  • Quasipolynomial size circuit classes

    Publication Year: 1992, Page(s):86 - 93
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (688 KB)

    Circuit complexity theory has tried to understand which problems can be solved by `small' circuits of constant depth. Normally `small' has meant `polynomial in the input size', but a number of recent results have dealt with circuits of size 2 to the log n0(1) power, or quasipolynomial size. The author summarizes the reasons for thinking about the complexity classes so introduce... View full abstract»

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  • How hard are sparse sets?

    Publication Year: 1992, Page(s):222 - 238
    Cited by:  Papers (11)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1116 KB)

    The frontier of knowledge about the structural properties of sparse sets is explored. A collection of topics that are related to the issue of how hard or easy sparse sets is surveyed. The strongest currently known results, together with the open problems that the results leave, are presented View full abstract»

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  • Bounding the complexity of advice functions

    Publication Year: 1992, Page(s):249 - 254
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (448 KB)

    It is known that every set A in P/poly has an advice function in PF (Σ2P(A)). It is shown that A also has an advice function in PF(NP(A) ⊕ Σ3P). From this bound, it is shown that separating Δ2P and Σ2 P relative to a set in P/poly is as ... 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 (9)
    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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