Proceedings of IEEE 9th Annual Conference on Structure in Complexity Theory

June 28 1994-July 1 1994

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  • Proceedings of IEEE 9th Annual Conference on Structure in Complexity Theory

    Publication Year: 1994
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    Freely Available from IEEE
  • Time, hardware, and uniformity

    Publication Year: 1994, Page(s):176 - 185
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (700 KB)

    We describe three orthogonal complexity measures: parallel time, amount of hardware, and degree of non-uniformity, which together parametrize most complexity classes. We show that the descriptive complexity framework neatly captures these measures using the parameters: quantifier depth, number of variable bits, and type of numeric predicates respectively. A fairly simple picture arises in which th... View full abstract»

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  • On the isomorphism problem for weak reducibilities

    Publication Year: 1994, Page(s):338 - 355
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1616 KB)

    The isomorphism conjecture states that all NP-complete sets are polynomial-time isomorphic while the encrypted complete set conjecture states that there is a p-one-way function f and an NP-complete set A such that A and f(A) are not polynomial-time isomorphic. We investigate these two conjectures for reducibilities weaker than polynomial-time. We show that: 1. Relative to reductions computed by on... View full abstract»

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  • Generic separations

    Publication Year: 1994, Page(s):139 - 145
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (432 KB)

    M. Blum and R. Impagliazzo (Proc. 28th IEEE Symposium on Foundations of Computer Science, pp. 118-126, 1987), using techniques of Hartmanis and Hemachandra (1991) and Rackoff (1982), showed that if P = NP then P(G) = NP(G)∩co-NP(G) = UP(G), where G is a generic oracle. They left open the question as to whether these collapses occur at higher levels of the polynomial-time hierarchy. We give a s... View full abstract»

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  • Alternation in interaction

    Publication Year: 1994, Page(s):294 - 303
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (760 KB)

    We study competing-prover one-round interactive proof systems. We show that one-round proof systems in which the first prover is trying to convince a verifier to accept and the second prover is trying to make the verifier reject recognized languages in NEXPTIME, and, with restrictions on communication and randomness, languages in NP. We extended the restricted model to an alternating sequence of k... View full abstract»

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  • On ultrafilters and NP

    Publication Year: 1994, Page(s):97 - 105
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (544 KB)

    The fusion method (A. Wigderson, 1993) is developed by exploring its similarities with the ultraproduct construction in model theory. We use this analogy to re-prove a result of M. Sipser (1984) regarding countable circuits, in a simpler way. In the finite case this analogy allows us to give a new characterization of co-NP in terms of the CLIQUE function. This gives a natural interpretation to the... View full abstract»

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  • Space lower-bounds for pseudorandom-generators

    Publication Year: 1994, Page(s):186 - 197
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (780 KB)

    Pseudorandom generation is a fundamental notion with many applications such as cryptography and deterministic simulation of random computation. A strong pseudorandom generator w.r.t. a tester class C is one that will “fool” any Turing-test in C to “believe” its output is truly random. We establish the first lower-bounds on the space complexity of general pseudorandom genera... View full abstract»

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  • Generalized CNF satisfiability problems and non-efficient approximability

    Publication Year: 1994, Page(s):356 - 366
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (768 KB)

    We use variants of the generalized CNF satisfiability problems SAT(S) of T.J. Schhaefer (1978) to characterize the efficient approximability of a number of basic NP and PSPACE-hard optimization problems in the literature. In contrast with the recent results, none of our proofs make use of interactive proof systems or of probabilistically checkable debate systems. In particular assuming P≠NP- or... View full abstract»

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  • Weakly hard problems

    Publication Year: 1994, Page(s):146 - 161
    Cited by:  Papers (7)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (880 KB)

    A weak completeness phenomenon is investigated in the complexity class E=DTIME(2linear). According to standard terminology, a language H is ⩽mP-hard for E if the set Pm(H), consisting of all languages A⩽mP H, contains the entire class E. A language C is ⩽m P-complete for E if it is ⩽m... View full abstract»

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  • The complexity of optimal queueing network control

    Publication Year: 1994, Page(s):318 - 322
    Cited by:  Papers (10)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (516 KB)

    We consider the classical problem of optimal control (routing and sequencing) of a network of queues. We prove that this problem is EXP-complete and, therefore, provably intractable. Similar results are established for restricted versions of the problem. A weaker result is also established for the restless bandit problem View full abstract»

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  • Some consequences of our failure to prove non-linear lower bounds on explicit functions

    Publication Year: 1994, Page(s):79 - 87
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (436 KB)

    Investigates the consequences of assuming that no explicit function has non-polynomial size Boolean circuit complexity. There are many consequences of this assumption. For example, it immediately proves that P does not equal NP. It also has ramifications for the length of certain interactive proofs View full abstract»

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  • Towards the parallel repetition conjecture

    Publication Year: 1994, Page(s):304 - 307
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (216 KB)

    We consider the behavior of the error probability of a two-prover one-round interactive protocol repeated n times in parallel. We point out the connection of this problem with the density form of Hales-Jewett's theorem in Ramsey theory. This allows us to show that the error probability converges to 0 as n→∞ View full abstract»

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  • NL/poly ⊆ ⊕L/poly

    Publication Year: 1994, Page(s):59 - 62
    Cited by:  Papers (9)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (228 KB)

    The article provides logspace analogs of the results of Valiant-Vazirani (L.G. Valiant and V.V. Vazirsni, 1986). We first show that solving STCONN for graphs with at most one st-path is essentially as hard as the general problem, via a probabilistic logspace reduction. We derive from it a nonuniform logspace reduction from NL to ⊕L View full abstract»

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  • On functions computable with nonadaptive queries to NP

    Publication Year: 1994, Page(s):43 - 52
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (736 KB)

    We study FP||NP, the class of functions that can be computed with nonadaptive queries to an NP oracle. We show that optimization problems stemming from the known NP complete sets, where the optimum is taken over a polynomially bounded range, are hard for FP||NP. This is related to (and, in some sense, extends) work of Z. Chen and S. Toda (1991). In addit... View full abstract»

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  • Unambiguous polynomial hierarchies and exponential size

    Publication Year: 1994, Page(s):106 - 115
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (736 KB)

    The classes NCk and ACk are defined by computational devices of polynomial size, i.e. by devices using a polynomially bounded number of gates or processors. We consider the case of exponential size, which results in classes between P and PSPACE. In this way, we get new characterizations of P and UP. The resulting relations of nondeterminism, unambiguity, and determinism to se... View full abstract»

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  • Constructive separation of classes of indistinguishable ensembles

    Publication Year: 1994, Page(s):198 - 204
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (468 KB)

    We construct ensembles that separate the classes of algorithmically, circuit, statistically, and perfect indistinguishable ensembles without cryptographic assumptions and present a generally usable technique for efficient deterministic simulation of resource bounded probabilistic Turing machines View full abstract»

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  • Collapsing degrees in subexponential time

    Publication Year: 1994, Page(s):367 - 382
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1056 KB)

    We show that there are subexponential deterministic time classes that have collapsing degrees. In particular, we prove the following: Let t be any effectively superpolynomial time bound. Then there is a set A∈DTIME(t) such that every set B∈degmp(A) is p-isomorphic to A View full abstract»

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  • Polynomial-time membership comparable sets

    Publication Year: 1994, Page(s):2 - 11
    Cited by:  Papers (10)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (764 KB)

    The paper introduces and studies a notion called polynomial-time membership comparable sets, which is a generalization of P-selective sets. For a function g, a set A is called polynomial-time g-membership comparable if there is a polynomial-time computable function f such that for any x1,…,xm with m⩾g(max{|x1 |,…,|xm|}), outputs b∈... View full abstract»

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  • Complexity classes defined via k-valued functions

    Publication Year: 1994, Page(s):224 - 234
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (712 KB)

    A lot of complexity classes can be characterized by posing some global acceptance condition on the computation trees produced by nondeterministic polynomial time machines. If the acceptance condition can be performed by a tree automaton, we obtain the concept of locally definable acceptance types (U. Hertrampf, 1992). This concept can be varied in different ways: if the acceptance condition depend... View full abstract»

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  • Relative to a random oracle, NP is not small

    Publication Year: 1994, Page(s):162 - 174
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (840 KB)

    The resource-bounded measure (J. Lutz, 1992) is an extension of classical measure theory which provides a probabilistic means of describing the relative sizes of complexity classes. Lutz proposed the hypothesis that NP does not have measure zero in the class E2=DTIME(2polynomial), meaning loosely that NP contains a non-negligible subset of exponential time. This hypothesis im... View full abstract»

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  • The complexity of learning with queries

    Publication Year: 1994, Page(s):324 - 337
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1012 KB)

    We survey recent research concerning the qualitative complexity of Angluin's (1993) model of learning with queries. In this model, there is a learner that tries to identify a target concept by means of queries to a teacher. Thus, the process can be naturally formulated as an oracle computation. Among the results we review there are: characterizations of the power of different learning protocols by... View full abstract»

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  • Downward separation fails catastrophically for limited nondeterminism classes

    Publication Year: 1994, Page(s):134 - 138
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (368 KB)

    The β hierarchy consists of sets βk=NP[log k n]⊆NP. Unlike collapses in the polynomial hierarchy and the Boolean hierarchy, collapses in the β hierarchy do not seem to translate up, nor does closure under complement seem to cause the hierarchy to collapse. For any consistent set of collapses and separations of levels of the hierarchy that respects P=β... View full abstract»

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  • Random debaters and the hardness of approximating stochastic functions

    Publication Year: 1994, Page(s):280 - 293
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1196 KB)

    A random probabilistically checkable debate system (RPCDS) for a language L consists of a probabilistic polynomial-time verifier V and a debate between Player 1, who aims to prove that the input x is in L, and Player 0, who selects a move uniformly at random from the set of legal moves. This model is a natural restriction of the PCDS model (Condon et al., Proc. 25th ACM Symposium on Theory of Comp... View full abstract»

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  • A direct product theorem

    Publication Year: 1994, Page(s):88 - 96
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (676 KB)

    Gives a general setting in which the complexity (or quality) of solving two independent problems is the product of the associated individual complexities. The authors then derive from this setting several concrete results of this type for decision trees and communication complexity View full abstract»

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  • Multi-prover encoding schemes and three-prover proof systems

    Publication Year: 1994, Page(s):308 - 317
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (812 KB)

    Suppose two provers agree in a polynomial p and want to reveal a single value y=p(x) to a verifier where m is chosen arbitrarily by the verifier. Whereas honest provers should be able to agree on any polynomial p the verifier wants to be sure that with any (cheating) pair of provers the value y he receives is a polynomial function of x. We formalize this question and introduce multi-prover (quasi-... View full abstract»

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