[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
    Request permission for commercial reuse | PDF file iconPDF (315 KB)
    Freely Available from IEEE
  • 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 (779 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.<<ETX>> 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 (356 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 P/sup NP/ is not contained in PP.<<ETX>> 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 (537 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 polynomial size. This is th... 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 (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (461 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/2/sup Theta /( square root log n) space while still running in polynomial time.<<ETX>> View full abstract»

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  • Fixed-parameter intractability

    Publication Year: 1992, Page(s):36 - 49
    Cited by:  Papers (16)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1262 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(n/sup c/), where c is a constant independent of the parameter y. They introduce a structure theory with which to address the apparent intractability of some parameterized problems, and they obtain completeness, density... 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 (469 KB)

    The authors separate NE from P/sub x/ (NP), where x=n/sup 0(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/sup A(1)/=EXP(EXP/sup A/=EXP). The authors separate EXP-low(1) from EXP-low by constructing a set A such that EXP/sup A(1)/=EXP and EXP/sup A/=EXP/sup EXP/.<<... View full abstract»

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  • Set bit enumeration is hard

    Publication Year: 1992, Page(s):58 - 70
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (895 KB)

    The polynomial-time function hierarchy is a function analog to the polynomial hierarchy and contains many interesting natural functions. Given the difficulties encountered so far in trying to develop feasible algorithms for these functions, the author seeks instead to construct feasible approximations. The author describes one such notion of approximation, set bit enumeration, which seems to be, b... 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 (891 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/sup SAT////sup (k)/<or=/sub m//sup P/-complete language to a language in P/sup SAT//(k-1)/ are obtained. It is proved that these probability bounds are tight unless PH collapses. Tight performance bounds on several randomized reductions between classes in the Boolean h... View full abstract»

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  • Quasipolynomial size circuit classes

    Publication Year: 1992, Page(s):86 - 93
    Cited by:  Papers (8)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (682 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 n/sup 0(1)/ power, or quasipolynomial size. The author summarizes the reasons for thinking about the complexity classes so introduced, surveys the... View full abstract»

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  • Circuits, matrices, and nonassociative computation

    Publication Year: 1992, Page(s):94 - 106
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1107 KB)

    It is shown that the formula and circuit evaluation problems in the nonassociative context capture natural complexity classes up to NP, thus extending the known result that the word problem over a groupoid is LOGCFL-complete. The problem of multiplying together matrices whose elements are taken from an algebraic structure more general than a semiring is defined and studied. It is shown that natura... 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 (9)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (293 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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  • 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 (446 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 Mod/sub k/P 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 can be computed... 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 (865 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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  • The quantum challenge to structural complexity theory

    Publication Year: 1992, Page(s):132 - 137
    Cited by:  Papers (11)  |  Patents (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (451 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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  • On the power of PP

    Publication Year: 1992, Page(s):138 - 143
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (379 KB)

    It is proved that MA is a subset of PP (relativizable) and that the intersection of AM/sup A/ and co-AM/sup A/ is not a subset of PP/sup A/ for some oracle A.<<ETX>> View full abstract»

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

    Publication Year: 1992, Page(s):144 - 154
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (622 KB)

    The algebraic structure of GapP and Hash P functions is introduced by formalizing them as power series ring and semiring, respectively. It is proved that for every invertible GapP function g, P/sup g/=P/sup 1/g/, and for all positive integers i, P/sup g/=P to the g/sup i/, power. Applying the Ladner theorem for functions, it is shown that P/sup s/=P/sup (s)/ for all S if and only if P=PP, where (S... 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 (1009 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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  • Descriptive complexity of Hash P functions

    Publication Year: 1992, Page(s):169 - 184
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1101 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 Hash 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 Hash P with interesting computational properties. In particular, using sy... 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 (589 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 tuple const... 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
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (930 KB)

    The classes of functions computable by uniform log-depth (NC/sup 1/) 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 definition... 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 (928 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 A has a universal relation, then for any set ... View full abstract»

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  • How hard are sparse sets?

    Publication Year: 1992, Page(s):222 - 238
    Cited by:  Papers (12)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1111 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.<<ETX>> View full abstract»

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  • On randomized reductions to sparse sets

    Publication Year: 1992, Page(s):239 - 242
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (268 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.<<ETX>> 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 (351 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.<<ETX>> View full abstract»

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