Proceedings Fifth Annual Structure in Complexity Theory Conference

8-11 July 1990

Filter Results

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»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • 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 (643 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»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • 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 (620 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.<<ETX>> View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • 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 (645 KB)

    The t-bounded instance complexity of a string x with respect to a set A, ic/sup t/(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 that if P not=NP, then for any polynomial t and constant c, ic/sup t/(x:A)>c... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • 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 (1289 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.<<ETX>> View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • 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 (670 KB)

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

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Privacy, additional information, and communication

    Publication Year: 1990, Page(s):55 - 65
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (847 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), the minimum amount of additional information revealed in any computation of ... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • 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 (696 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 Omega (n/sup 5/4/) lower bound on the randomized decision tree complexi... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • 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 (657 KB)

    TC/sup 0/ is the class of functions computable by polynomial-size, constant-depth formulae with threshold gates. Read-once TC/sup 0/ (RO-TC/sup 0/) is the subclass of TC/sup 0/ 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-TC/sup 0/. This relationship between th... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • 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»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Perfect hashing, graph entropy, and circuit complexity

    Publication Year: 1990, Page(s):91 - 99
    Cited by:  Papers (15)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (720 KB)

    It is shown that approximate compaction can be efficiently performed in constant parallel time using perfect hash functions. This allows it to be shown that polylogarithmic-threshold functions are in linear AC/sup o/. Next, it is shown that the information-theoretic notion of graph entropy captures some aspect of the difficulty of computing Boolean functions. This is used to derive superlinear low... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • 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 (816 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»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • 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 (629 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 there exist languages in EXPSPACE which... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • 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 (611 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»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • 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 (654 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.<<ETX>> View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • 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 (782 KB)

    Consideration is given to polynomial-time machines. Among these classes are EP and PP. The authors prove P/sup EP(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 of suc... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • A very hard log space counting class

    Publication Year: 1990, Page(s):154 - 168
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1393 KB)

    Consideration is given to the logarithmic space counting classes Hash L, opt-L, and span-L, which are defined analogously to their polynomial-time counterparts. Complete functions are obtained for these three classes in terms of graphs and finite automata. It is shown that Hash L and opt-L are both contained in NC/sup 2/, but that, surprisingly, span-L seems to be much harder counting class than H... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • The Boolean hierarchy and the polynomial hierarchy: a closer connection

    Publication Year: 1990, Page(s):169 - 178
    Cited by:  Papers (10)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (847 KB)

    It is shown that if the Boolean hierarchy collapses to level k, then the polynomial hierarchy collapses to BH/sub 3/(k), where BH/sub 3/(k) is the kth level of the Boolean hierarchy over Sigma /sub 2//sup p/. This result is significant in two ways. First, the theorem says that a deeper collapse of the Boolean hierarchy implies a deeper collapse of the polynomial hierarchy. This results also points... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • 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 (435 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»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • 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 (1190 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.<<ETX>> View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Extensions to Barrington's M-program model

    Publication Year: 1990, Page(s):200 - 209
    Cited by:  Papers (5)
    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»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • 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 (1020 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 sigma of a very restricted form, whose set of finite models corresponds to the set of strings recognized by M. Specifically, sigma is in the theory of addition restricted t... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • 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 (656 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»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • 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 (1021 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, k(n)=O(log n) queries to an NP-complete set (k(n)=O(1) queries to an NP-hard set) are more powerful than k(n)-1 queries, ... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • 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»

    Full text access may be available. Click article title to sign in or learn about subscription options.