Proceedings Fifth Annual Structure in Complexity Theory Conference

8-11 July 1990

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Displaying Results 1 - 25 of 33
  • On polynomial time bounded truth-table reducibility of NP sets to sparse sets

    Publication Year: 1990
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (32 KB)

    Summary form only given. It is proved that if P not=NP, then there exits a set in NP that is polynomial-time bounded truth-table reducible to no sparse set. By using the technique proving this result, intractability of several number theoretic decision problems, i.e. decision problems defined naturally from number theoretic problems, is investigated. It is shown that for those number theoretic dec... View full abstract»

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  • The computational complexity of universal hashing

    Publication Year: 1990
    Cited by:  Papers (8)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (75 KB)

    Summary form only given. Any implementation of Carter-Wegman universal hashing from n-b strings to m-b strings requires a time-space tradeoff of TS= Omega (nm). The bound holds in the general Boolean branching program model, and thus in essentially any model of computation. As a corollary, computing a+b*c in any field F requires a quadratic time-space tradeoff, and the bound holds for any represen... View full abstract»

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  • Extensions to Barrington's M-program model

    Publication Year: 1990, Page(s):200 - 209
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (965 KB)

    Groupoids are used instead of monoids to extend D.A. Barrington's (1988) successful polynomial length program over a monoid computation model to characterize complexity classes TC and LOGCFL. Further allowing groupoid families instead of fixed groupoids, deterministic and nondeterministic logarithmic space are also characterized. Several language classes arising from extended programs over Abelian... View full abstract»

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  • Quantifiers and approximation

    Publication Year: 1990
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (51 KB)

    Summary form only given. An investigation is made of the relationship between logical expressibility of NP optimization problems and their approximation properties. It is shown that many important optimization problems do not belong to MAX NP and that in fact there are problems in P which are not in MAX NP. The problems considered fit naturally in a new complexity class called MAX II/sub 1/. It is... View full abstract»

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  • Proceedings. Fifth Annual Structure in Complexity Theory Conference (Cat. No.90CH2899-3)

    Publication Year: 1990
    Request permission for commercial reuse | PDF file iconPDF (312 KB)
    Freely Available from IEEE
  • Privacy, additional information, and communication

    Publication Year: 1990, Page(s):55 - 65
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (720 KB)

    Two parties which hold n-b inputs x and y , respectively, wish to cooperate in computing a predetermined function f(x,y). For most functions f, this task cannot be accomplished privately, namely, without revealing some additional information to at least one of the parties. The authors initiate a quantitative study of T(f View full abstract»

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  • An oracle separating ⊕P from PPPH

    Publication Year: 1990, Page(s):295 - 298
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (264 KB)

    The existence of an oracle A such that ⊕PA is not contained in PPPHA is proved. This separation follows in a straightforward manner from a circuit complexity result, which is also proved: to compute the parity of n inputs, any constant depth circuit consisting of a single threshold gate on top of ANDs and ORs requires exponential size in n View full abstract»

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  • On bounded round multiprover interactive proof systems

    Publication Year: 1990, Page(s):45 - 54
    Cited by:  Papers (7)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (560 KB)

    Bounded round multiprover interactive proof systems (MIPs) are compared with unbounded round interactive proof systems (IPSs). It is shown that for any constant ε, any language accepted by an unbounded round IPS has a bounded round, two-prover MIP that has error probability ε, resolving an open problem of L. Fortnow et al. (1988). To obtain this result, it is shown that a certain one-rou... View full abstract»

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  • On read-once vs. multiple access to randomness in logspace

    Publication Year: 1990, Page(s):179 - 184
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (368 KB)

    In the correct definition of randomized space-bounded computation, the machine has access to a random coin. The coin can be flipped at will, but outcomes of previous coin flips cannot be recalled unless they are saved in the machine's limited memory. In contrast to this read-once mechanism of accessing the random source, one may consider Turing machines which have access to a random tape. Here, th... View full abstract»

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  • Non-uniform complexity classes and random languages

    Publication Year: 1990, Page(s):110 - 119
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (524 KB)

    A language A is considered to be random for a class C if for every language B in C the fraction of the strings where A and B coincide is approximately 1/2. R.E. Wilber (1983) showed that there exist tight space and time hierarchies of random languages. These results are extended to nonuniform complexity classes, and a result of D.T. Huynh (1987) proving that the... View full abstract»

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  • A note on relativizing complexity classes with tally

    Publication Year: 1990, Page(s):287 - 294
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (564 KB)

    T. Long and A. Selman (1986) proved that, for most familiar pairs of complexity classes, separating the classes with a tally oracle is no easier than truly separating the classes. For relativized worlds, it is shown in this work that even for such pairs of classes, collapsing the classes with a tally oracle is easier than truly collapsing the classes, and it is demonstrated for the first time that... View full abstract»

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  • Complexity classes with advice

    Publication Year: 1990, Page(s):305 - 315
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (644 KB)

    A novel concept of nonuniform complexity classes is presented, from which a uniform way of describing known complexity classes is obtained. The usual nonuniform complexity classes introduced by R.M. Karp and R.J. Lipton are modified in two ways: first, not only classes of advice functions defined by pure length bounds are considered, but also limiting the complexity of these functions. In a second... View full abstract»

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  • On sets with efficient implicit membership tests

    Publication Year: 1990, Page(s):11 - 19
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (524 KB)

    The complexity of implicit membership testing is characterized in terms of the well-known complexity class OptP, optimization polynomial time. It is concluded that many complex sets have polynomial-time implicit membership tests. Thus, the complexity of implicit membership testing is closely related to the complexity of optimization View full abstract»

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  • Unambiguity of circuits

    Publication Year: 1990, Page(s):130 - 137
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (552 KB)

    The concept of unambiguity of circuits is considered. Several classes of unambiguous circuit families within the NC-hierarchy are introduced and related to unambiguous automata and to PRAMs with exclusive write-access. In particular, it is shown that CREW-TIME (log n)=UnambAC View full abstract»

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  • E-mail and the unexpected power of interaction

    Publication Year: 1990, Page(s):30 - 44
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1112 KB)

    The LFKN protocol, interactive proofs, complexity classes, relativized separation, arithmetization of Boolean formulas, program verification, multiple provers, circuit reductions and publishable proofs, and space-bounded interactive proofs are discussed. An examination is also made of e-mail ethics View full abstract»

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  • The Boolean hierarchy and the polynomial hierarchy: a closer connection

    Publication Year: 1990, Page(s):169 - 178
    Cited by:  Papers (9)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (712 KB)

    It is shown that if the Boolean hierarchy collapses to level k , then the polynomial hierarchy collapses to BH3(k ), where BH3(k) is the kth level of the Boolean hierarchy over Σ2p. This result is significant in two ways. First, the theorem says that a deeper collapse of the Boolean hierarchy implies a deeper col... View full abstract»

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  • Lower bounds on random-self-reducibility

    Publication Year: 1990, Page(s):100 - 109
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (692 KB)

    The limitations of random-self-reducibility are studied, and several negative results are proved. For example, it is shown unconditionally that random Boolean functions do not have random self-reductions, even of a quite general nature. For several natural, but less general, classes of random self-reductions, it is shown that, unless the polynomial hierarchy collapses, nondeterministic polynomial-... View full abstract»

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  • Circuit size relative to pseudorandom oracles

    Publication Year: 1990, Page(s):268 - 286
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1152 KB)

    Deterministic and nondeterministic circuit-size complexities are compared to deterministic and nondeterministic time complexities in the presence of pseudorandom oracles. Certain separations are shown to hold relative to every pspace-random oracle A, and relative to almost every oracle A∈ESPACE. In fact, these separations are shown to hold for almost every n. Since ... View full abstract»

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  • On the power of randomness in the decision tree model

    Publication Year: 1990, Page(s):66 - 77
    Cited by:  Papers (2)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (584 KB)

    Results suggest that there are relations between the decision tree complexity of a Boolean function and its symmetry. A central conjecture is that for any monotone graph property the randomized decision tree complexity does not differ from the deterministic one with more than a constant factor. The authors improve on V. King's Ω(n5/4) lower bound on the randomized decisio... View full abstract»

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  • On separating complexity classes

    Publication Year: 1990, Page(s):299 - 304
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (468 KB)

    Some observations that suggest that certain separation results based on the use of random oracles will not provide information about the separation of the corresponding unrelativized classes (without some additional hypothesis) are presented. It is observed that J.-Y Cai's (1989) result showing that for almost every set A, PH(A)≠PSPACE(A), does not address the open qu... View full abstract»

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  • Structural properties of nondeterministic complete sets

    Publication Year: 1990, Page(s):3 - 10
    Cited by:  Papers (11)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (548 KB)

    Two aspects of the structure of complete sets for NE and larger nondeterministic time classes are surveyed. First, differences between complete sets arising from various polynomial-time reductions are proved. Immunity properties of these complete sets are then considered. It is shown that NE-complete sets (and their complements) have dense E subsets and dense UP subsets. All of these results hold ... View full abstract»

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  • Bounded arithmetic and computational complexity

    Publication Year: 1990, Page(s):186 - 199
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1000 KB)

    A survey of certain characterizations of complexity classes in an algebraic, machine-independent manner is presented, together with some applications to weak theories of arithmetic and higher-order functionals. Function algebras are examined, and hierarchies are defined. Bounded arithmetic theories are presented View full abstract»

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  • Width-bounded reducibility and binary search over complexity classes

    Publication Year: 1990, Page(s):122 - 129
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (524 KB)

    A notion of width-bounded reducibility is introduced. Width-bounded reducibility provides a circuit-based realization of Ruzzo-Simon-Tompa reducibility and allows that notion of reducibility to be generalized. It is shown that reductions of simultaneously restricted width and depth provide a characterization of binary search over complexity classes, as introduced by K. Wagner (1989) and S. Buss an... View full abstract»

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  • On the instance complexity of NP-hard problems

    Publication Year: 1990, Page(s):20 - 27
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (540 KB)

    The t-bounded instance complexity of a string x with respect to a set A, ict(x:A), is defined as the size of the smallest program (roughly, Turing machine) that runs in time t, decides x correctly, and makes no mistakes on other strings (don't know answers are permitted). For certain conditions on A, it is proved th... View full abstract»

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  • The quantifier structure of sentences that characterize nondeterministic time complexity

    Publication Year: 1990, Page(s):210 - 222
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (864 KB)

    The well-known model theoretic characterization of nondeterministic time complexity is studied. It is shown that for every nondeterministic Turing machine M of time complexity T(n), there is an existential second-order sentence σ of a very restricted form, whose set of finite models corresponds to the set of strings recognized by M. Specifically, σ i... View full abstract»

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