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
  • 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 (844 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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  • DSPACE(n)=?NSPACE(n): a degree theoretic characterization

    Publication Year: 1995, Page(s):315 - 323
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (764 KB)

    It is shown that the following are equivalent: 1. DSPACE(n)=NSPACE(n). 2. There is a ⩽m1-NL-degree that coincides with a ⩽m1-L degree. 3. For every class C closed under logspace reductions the ⩽m1-NL-complete degree of C coincides with the ⩽m1-L-complete degree of C 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 (412 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 +, -, × 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 “uniqu... 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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  • A personal view of average-case complexity

    Publication Year: 1995, Page(s):134 - 147
    Cited by:  Papers (35)
    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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  • 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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  • 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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  • 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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  • 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 (336 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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  • 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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  • 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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  • 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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  • 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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  • 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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  • 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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  • 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 (820 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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  • 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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  • 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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  • An excursion to the Kolmogorov random strings

    Publication Year: 1995, Page(s):197 - 203
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (528 KB)

    We study the set of resource bounded Kolmogorov random strings: R t={x|Kt(x)⩾|x|} for t a time constructible function such that t(n)⩾2(n2) and t(n)∈2(nO(1)). We show that the class of sets that Turing reduce to Rt has measure 0 in EXP with respect to the resource-bounded measure introduced by Lutz (1992). From this we conclude that Rt 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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  • 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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  • Resource-bounded Baire category: a stronger approach

    Publication Year: 1995, Page(s):182 - 192
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (824 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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  • 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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