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[1988] Proceedings. Structure in Complexity Theory Third Annual Conference

14-17 June 1988

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  • Proceedings: Structure in Complexity Theory Third Annual Conference (Cat. No.88CH2542-9)

    Publication Year: 1988
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    Freely Available from IEEE
  • Relativized polynomial time hierarchies having exactly K levels

    Publication Year: 1988
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (36 KB)

    Summary form only given. The relativization of the Meyer-Stockmeyer polynomial-time hierarchy is treated. The proof techniques combine an encoding scheme with probabilistic arguments.<> View full abstract»

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  • The power of counting

    Publication Year: 1988, Page(s):2 - 9
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (452 KB)

    An overview of applications and variations of counting in structural complexity theory is provided. It is argued that the capacity for exact counting is closely related with the capacity for nondeterministic complementation. Relations between counting classes and classes requiring uniqueness, such as UP, are discussed, as well as approximate counting and relativized results View full abstract»

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  • Juris Hartmanis: building a department-building a discipline

    Publication Year: 1988, Page(s):135 - 137
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (216 KB)

    The author covers Hartmanis' activities during the middle years of his career, from 1965, when he came to Cornell as chairman of a newly formed Computer Science Department, until 1978. He discusses how Hartmanis developed a department and, at the same time, strongly influenced the direction of computer science as a distinct discipline. He outlines the direction of Hartmanis' research in complexity... View full abstract»

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  • The complexity of ranking

    Publication Year: 1988, Page(s):204 - 212
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (696 KB)

    It is shown that ranking languages accepted by one-way unambiguous auxiliary pushdown automata are in NC(2). Negative results about ranking for several classes of simple languages are proved. It is shown that C is rankable in deterministic polynomial time if P=#P, where C is any of the following classes of languages: (1) languages accepted by logtime-bounded nondetermi... View full abstract»

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  • Juris Hartmanis: the beginnings of computational complexity

    Publication Year: 1988, Page(s):128 - 134
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (468 KB)

    The author discusses the early period of Hartmanis' research. He examines the origins of the concepts presented in the early papers and the influence of and effects on other research. Some of the important results are considered View full abstract»

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  • Space bounded probabilistic game automata

    Publication Year: 1988, Page(s):162 - 174
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1144 KB)

    Results on the power of space-bounded probabilistic game automata are presented. Space-bounded analogs of Arthur-Merlin games and interactive proof systems are considered for bounded random game automata with complete and partial information. A consequence of the results is that any language recognizable in deterministic exponential time has an interactive proof that uses only logarithmic space. T... View full abstract»

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  • Enumerative counting is hard

    Publication Year: 1988, Page(s):194 - 203
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (484 KB)

    An n-variable Boolean formula can have anywhere from 0 to 2n satisfying assignments. The question of whether a polynomial-time machine, given such a formula, can reduce this exponential number of possibilities to a small number of possibilities is explored. Such a machine is called an enumerator, and it is proved that if there is a good polynomial-time enumerator for #P (i.e. o... View full abstract»

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  • Two applications of complementation via inductive counting

    Publication Year: 1988, Page(s):116 - 125
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (592 KB)

    A recent proof that nondeterministic space-bounded complexity classes are closed under complementation is used to develop two further applications of the inductive counting technique. An errorless probabilistic algorithm is given for the undirected graph s-t connectivity problem that runs in O(log n) space and polynomial expected time, and it is shown that the class LOGC... View full abstract»

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  • On the power of multi-power interactive protocols

    Publication Year: 1988, Page(s):156 - 161
    Cited by:  Papers (7)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (408 KB)

    A simple characterization of the power of the multipower model in terms of probabilistic oracle Turing machines is given. It is shown that languages that have single-prover interactive protocols also have two prover-bounded round protocols and that languages that have multiprover interactive protocols have two prover protocols and three prover-bounded round protocols. An oracle is given relative t... View full abstract»

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  • Distinguishing bounded reducibilities by sparse sets

    Publication Year: 1988, Page(s):181 - 191
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (760 KB)

    Two kinds of restrictions on the power of oracle machines have arisen when considering resource-bounded reducibilities. The first restricts the underlying machine model used for reduction with respect to the number of queries allowed on each input (e.g. bounded-query reducibilities), the way the answers to the queries are to be used (e.g. conjunctive and disjunctive reducibilities), and the depend... View full abstract»

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  • Nondeterministic space is closed under complementation

    Publication Year: 1988, Page(s):112 - 115
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (236 KB)

    It is shown that nondeterministic space s(n) is closed under complementation for s(n) greater than or equal to log n. It immediately follows that the context-sensitive languages are closed under complementation. The proof is an offshoot of work in first-order expressibility View full abstract»

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  • Two decades of applied Kolmogorov complexity: in memoriam Andrei Nikolaevich Kolmogorov 1903-87

    Publication Year: 1988, Page(s):80 - 101
    Cited by:  Papers (15)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (2204 KB)

    The authors provide an introduction to the main ideas of Kolmogorov complexity and survey the wealth of useful applications of this notion. It is based on a theory of information content of strings, intuitively, that the amount of information in a finite string is the size (i.e. number of bits) of the smallest program that, started with a blank memory, computes the string and then terminates. The ... View full abstract»

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  • Reductions among prediction problems: on the difficulty of predicting automata

    Publication Year: 1988, Page(s):60 - 69
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (832 KB)

    Given examples of words accepted and rejected by an unknown automaton, the question of whether there is an algorithm that in a feasible amount of time will learn to predict which words will be accepted by the automaton is examined. A notion of prediction-preserving reducibility is developed, and it is shown that if DFAs are predictable, then so are all languages in logspace. In particular, the pre... View full abstract»

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  • On polynomial and generalized complexity cores

    Publication Year: 1988, Page(s):236 - 250
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1148 KB)

    Recent results on polynomial complexity cores, their complexity, density, and structure and their counterparts on proper hard cores are surveyed and interpreted. An approach to generalized complexity cores that is almost axiomatic in nature is included in the discussion. The purpose is to provide an integrated presentation of this material View full abstract»

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  • The polynomial time hierarchy collapses if the Boolean hierarchy collapses

    Publication Year: 1988, Page(s):278 - 292
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (948 KB)

    It is shown that if the Boolean hierarchy (BH) collapses, then there exists a sparse set S such that co-NP⊆NPS, and therefore the polynomial-time hierarchy (PH) collapses to a subclass of ΔP/3. Since the BH is contained in PNP, these results relate the internal structure of PNP to the structure of the PH as a whole. Other conditions that imply ... View full abstract»

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  • Logspace self-reducibility

    Publication Year: 1988, Page(s):40 - 46
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (528 KB)

    A definition of self-reducibility is proposed to deal with logarithmic space complexity classes. A general property derived from the definition is used to prove known results comparing uniform and nonuniform complexity classes below polynomial time, and to obtain novel ones regarding nondeterministic nonuniform classes and reducibility to context-free languages View full abstract»

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  • On tally relativizations of BP-complexity classes

    Publication Year: 1988, Page(s):10 - 18
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (548 KB)

    The concept of a random tally set is introduced. Relativization of BP-complexity classes with respect to a tally oracle is considered. Certain results are established and used to show that the BP-polynomial-time hierarchy has properties faithfully reflecting those of the polynomial-time hierarchy; that is, the properties established by relativization yield results for unrelativized cases View full abstract»

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  • Juris Hartmanis: fundamental contributions to isomorphism problems

    Publication Year: 1988, Page(s):138 - 154
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1068 KB)

    The author surveys Hartmanis' contributions to isomorphism problems. These problems are primarily of two forms: first, isomorphism problems for restricted programming systems, including the Hartmanis-Baker conjecture that all polynomial time programming systems are polynomially isomorphic; and second, the research on isomorphisms, and particularly polynomial time isomorphisms, for complete problem... View full abstract»

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  • An oracle characterization of the counting hierarchy

    Publication Year: 1988, Page(s):213 - 223
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (640 KB)

    Certain properties of the polynomial-time counting hierarchy (CH) introduced by K. Wagner (1986) are investigated. The closure under Boolean operations of the classes in CH is studied, and a characterization of the hierarchy in terms of nondeterministic and probabilistic machines with access to oracles is proved. The concept of lowness is extended to the classes in CH, providing a way to character... View full abstract»

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  • Pseudorandom sources for BPP

    Publication Year: 1988, Page(s):175 - 180
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (420 KB)

    A computational problem is considered feasible if it can be solved in polynomial time with arbitrarily low probability of error by a probabilistic algorithm. In principle, such an algorithm requires a generous (infinite) source of independent random bits, but it is generally assumed that it will perform equally well when supplied with a deterministically computed sequence of pseudorandom bits. The... View full abstract»

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  • Kolmogorov complexity and degrees of tally sets

    Publication Year: 1988, Page(s):102 - 111
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (592 KB)

    A recent paper by S. Tang and R. Book (1988) initiated a study of the classes of sets which are equivalent to tally sets or sparse sets, under varying notions of reducibility. A number of interesting results are proved, and many additional questions are posed and left open. The authors investigate some of these questions and show that they are equivalent to each other and are closely related to ot... View full abstract»

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  • On the theory of the PTIME degrees of the recursive sets

    Publication Year: 1988, Page(s):252 - 257
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (448 KB)

    An interpretation is given of first-order arithmetic in the theory of the PTIME degrees of the recursive sets, ordered under PTIME Turing reducibility (<REC, ⩽p>). This characterizes the Turing degree of the first-order theory of <REC, ⩽ p>. In particular, it is not decidable View full abstract»

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  • Trading reversals for alternation

    Publication Year: 1988, Page(s):70 - 77
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (552 KB)

    The relation between reversals and alternation is studied in two simple models of computation: the two-counter machine with a one-way input tape whose counters make only one reversal (1-reversal 2CM) and the one-way pushdown automation whose pushdown store makes only one reversal (1-reversal PDA). It is known that nondeterministic 1-reversal 2CMs (and, more generally, 1-reversal mCMs when there ar... View full abstract»

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  • Cook is faster than Karp: a study of reducibilities in NP

    Publication Year: 1988, Page(s):293 - 302
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (600 KB)

    It is unknown whether Cook reducibility of a set A to a set B (i.e. reduction of A to B by a Turing machine operating in polynomial time with free procedural calls to an algorithm for B), is more general than Karp reducibility (i.e. reduction of A to B by a function computable in polynomial time) on sets in NP. While it is conjectured ... View full abstract»

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