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
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    Freely Available from IEEE
  • 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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  • Impossibilities and possibilities of weak separation between NP and exponential time

    Publication Year: 1990, Page(s):245 - 253
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (444 KB)

    Two complexity classes are considered to be weakly separated if they are separated but there is no immune set in the difference of the classes. It is shown that the weak separation between NP and exponential time, together with the inclusion and the weak separation simultaneously in both directions (weak incomparability), is not possible in any relativized or nonrelativized world. On the other han... View full abstract»

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  • A very hard log space counting class

    Publication Year: 1990, Page(s):154 - 168
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (1188 KB)

    Consideration is given to the logarithmic space counting classes polynomial-time counterparts. Complete functions are obtained for these three classes in terms of graphs and finite automata. It is shown that surprisingly, span-L seems to be much harder counting class than #L and opt-L. It is demonstrated that span-L-functions can be computed in polynomial time if and only if P=NP=PH=P(#P), i.e if ... View full abstract»

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  • A survey on counting classes

    Publication Year: 1990, Page(s):140 - 153
    Cited by:  Papers (11)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (664 KB)

    Consideration is given to polynomial-time machines. Among these classes are EP and PP. The authors prove PEP[log] 25 PP, investigate the Boolean closure BC(EP) of EP, and give a relativization principle which allows them to completely separate BC(EP) in a suitable relativized world and to give simple proofs for known relativization results. Further results concerning the relationships o... 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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  • 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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  • 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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  • 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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  • Some connections between bounded query classes and nonuniform complexity

    Publication Year: 1990, Page(s):232 - 243
    Cited by:  Papers (23)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (856 KB)

    It is shown that if there is a polynomial-time algorithm that tests k(n)=O(log n) points for membership in a set A by making only k(n)-1 adaptive queries to an oracle set X, then A belongs to NP/poly intersection co-NP/poly (if k(n)=O(1) then A belong to P/poly). In particular, ... 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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  • 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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  • 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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  • 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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  • 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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  • 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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  • P-productivity and polynomial time approximations

    Publication Year: 1990, Page(s):254 - 265
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (888 KB)

    P-productivity and p-creativity are useful concepts for studying polynomial-time approximations to sets not in P. It is shown that every deterministic O(T(n)) time computable p-productive set for P contains infinite subsets in P and moreover does not contain a largest P subset, where T is any time constructible function which dominates all polynomials. ... 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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  • Circuits, pebbling and expressibility

    Publication Year: 1990, Page(s):223 - 230
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (564 KB)

    Characterizations of nondeterministic complexity classes such as NP and PSPACE and the classes in the polynomial-time hierarchy in the two-person pebble game model are given. It is shown that the role-switches resource in the pebble games closely models the levels of the polynomial hierarchy. These characterizations are made possible by explicitly considering circuit size in the pebbling character... 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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  • On read-once threshold formulae and their randomized decision tree complexity

    Publication Year: 1990, Page(s):78 - 87
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (544 KB)

    TC0 is the class of functions computable by polynomial-size, constant-depth formulae with threshold gates. Read-once TC0 (RO-TC0) is the subclass of TC0 which restricts every variable to exactly one occurrence in the formula. The main result is a tight linear lower bound on the randomized decision tree complexity of any function in RO-TC0. Thi... View full abstract»

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