[1989] Proceedings. Structure in Complexity Theory Fourth Annual Conference

19-22 June 1989

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Displaying Results 1 - 25 of 31
  • Hardness vs. randomness-a survey

    Publication Year: 1989
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (28 KB)

    Summary form only given, as follows. Probabilistic algorithms are considered to be as practical as deterministic ones for solving computational problems. However, obvious practical and theoretical considerations have led to the questions of when, and at what cost, can one get rid of the randomness in these algorithms. A natural direction was to follow the lead of real computers and use determinist... View full abstract»

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  • Proceedings. Structure in Complexity Theory Fourth Annual Conference (Cat. No.89CH2745-8)

    Publication Year: 1989
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    Freely Available from IEEE
  • The isomorphic conjecture fails relative to a random oracle

    Publication Year: 1989
    Cited by:  Papers (13)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (29 KB)

    Summary form only given, as follows. L. Berman and H. Hartmanis (1977) conjectured that there is a polynomial-time computable isomorphism between any two languages m-complete (Karp complete) for NP. D. Joseph and P. Young (1985) discovered a structurally defined class of NP-complete sets and conjectured that certain of these sets (the K/sub f//sup k,/s) are not isomorphic to the standard NP-comple... View full abstract»

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  • On the theory of average case complexity

    Publication Year: 1989
    Cited by:  Papers (8)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (29 KB)

    Summary form only given, as follows. The authors take the next step in developing the theory of average case complexity initiated by L.A. Levin. Previous work has focused on the existence of complete problems. The present authors widen the scope to other basic questions in computational complexity. Their results include: (1) the equivalence of search and decision problems in the context of average... View full abstract»

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  • The minimum consistent DFA problem cannot be approximated within any polynomial

    Publication Year: 1989
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (30 KB)

    Summary form only given, as follows. The minimum consistent DFA problem is that of finding a DFA with as few states as possible that is consistent with a given sample (a finite collection of words, each labeled as to whether the DFA found should accept or reject). Assuming that P not=NP, it is shown that for any constant k, no polynomial-time algorithm can be guaranteed to find a consistent DFA of... View full abstract»

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  • On polynomial time Turing and many-one completeness in PSPACE

    Publication Year: 1989, Page(s):15 - 23
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (540 KB)

    The different between polynomial-time-Turing- and polynomial-time-many-one-completeness notions in PSPACE is shown from each of the following assumptions: (i) a randomized completeness notion differs from a deterministic one in PSPACE; and (ii) PSPACE has a dense set, almost every element of which is hard to produce by any polynomial-time computation. A. Mayer and M. Paterson (Tech. Rep. MIT/LCS/T... View full abstract»

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  • Oracles for structural properties: the isomorphism problem and public-key cryptography

    Publication Year: 1989, Page(s):3 - 14
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (840 KB)

    There exists an oracle, relative to which P ≠ NP and each of the following properties hold: (i) all Σp2-complete sets are p-isomorphic; (ii) P-inseparable pairs of sets in NP do not exist; (iii) intractable public-key cryptosystems do not exist; and (iv) NP-complete sets are closed under union of disjoint sets. Remarkably, these properties all follow from one oracle ... View full abstract»

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  • On the structure of bounded queries to arbitrary NP sets

    Publication Year: 1989, Page(s):250 - 258
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (476 KB)

    The author examines hierarchies built with arbitrary sets in NP. He determines when these hierarchies are proper and how they relate to the Boolean hierarchy (BH) and the query hierarchy (QH). He studies these questions in the setting of U. Schoning's high-low sets (see J. Comput. Syst. Sci., vol.27, p.14-28 (1983)). He produces some results about the hierarchies built with arbitrary NP sets. Thes... View full abstract»

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  • The complexity of circuit value and network stability

    Publication Year: 1989, Page(s):114 - 123
    Cited by:  Papers (7)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (744 KB)

    A method for nontrivially restricting fanout in a circuit is developed. The complexity of the circuit value problem and a new problem, network stability, is studied when fanout is limited. This leads to new classes or problems within P. It is conjectured that the new classes are different from P and incomparable to NC. One of these classes, CC, contains several natural complete problems, including... View full abstract»

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  • Separating complexity classes related to certain input oblivious logarithmic space-bounded Turing machines

    Publication Year: 1989, Page(s):240 - 249
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (480 KB)

    It is proved that oblivious simultaneously linear access-time and logarithmic space-bounded nondeterministic Turing machines are more powerful than deterministic ones. All the corresponding complexity classes are separated from each other View full abstract»

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  • The generalized Kolmogorov complexity of sets

    Publication Year: 1989, Page(s):186 - 194
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (480 KB)

    Recent work has shown that it is useful to consider new variants of time-bounded Kolmogorov complexity. The author reviews that work, presents the new definitions, and studies the basic properties of these measures. He deals with the function KL, which measures the complexity of the simplest strings in the language L and with sets of the form KUv[<... View full abstract»

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  • The complexity of iterated multiplication

    Publication Year: 1989, Page(s):104 - 111
    Cited by:  Papers (13)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (552 KB)

    The complexity of multiplying together n elements of a group G is studied. It is observed that as G ranges over a sequence of well-studied groups, the iterated multiplication problem is complete for corresponding well-studied complexity classes. Furthermore, the notion of completeness in question is extremely low-level and algebraic. The issue of uniformity is investigat... View full abstract»

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  • On finding locally optimal solutions

    Publication Year: 1989, Page(s):132 - 137
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (312 KB)

    The problem of finding locally optimal solutions to combinatorial problems in the framework of polynomial-time local search as defined by D.S. Johnson et al. (J. Comput. Syst. Sci., vol.37, no.1, p.79-100, Aug. 1988) is considered. A PLS-complete problem such that the problem of verifying local optimality can be solved in LOGSPACE is exhibited. For all previously known PLS-complete problems, verif... View full abstract»

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  • On the relativized power of additional accepting paths

    Publication Year: 1989, Page(s):216 - 224
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (584 KB)

    The author defines Uk(n)P as the class of languages in NP that are accepted by machines with at most k(n) accepting paths on each input of length n. Then P ⊆ UP ⊆ Uk(n)P ⊆ Uk(n)+1P ⊆ FewP $4 for every polynomial k(n)⩾2, where FewP is the class of languages in NP that are accepted by machines with ... View full abstract»

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  • The complexity types of computable sets

    Publication Year: 1989, Page(s):231 - 239
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (772 KB)

    The fine structure of time complexity classes for random access machines is analyzed. It is proved that a complexity type C contains sets A,B which are incomparable with respect to polynomial-time reductions if and only if it is not true that C ⊆ P, and that there is a complexity type C that contains a minimal pair with respect to polynomial-time reductions. The fine structu... View full abstract»

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  • Inductive reasoning and Kolmogorov complexity

    Publication Year: 1989, Page(s):165 - 185
    Cited by:  Papers (12)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (1876 KB)

    The inductive reasoning concepts of R.J. Solomonoff (Inf. Control. vol.7, p.1-22, 224-254, 1964) are considered. The thesis is developed that Solomonoff's method is fundamental in the sense that many other induction principles can be viewed as particular ways to obtain computable approximations to it. This is demonstrated explicitly in the cases of E.M. Gold's (1967, 1978) paradigm for inductive i... View full abstract»

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  • The P-T-degrees of the recursive sets: lattice embeddings, extensions of embeddings and the two quantifier theory

    Publication Year: 1989, Page(s):68 - 76
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (808 KB)

    It has been shown in the literature that the two basic nondistributive lattices can be embedded in Rpt, the polynomial-time turing degrees of the recursive sets. The authors introduce more general techniques to extend these results to show that every recursive lattice can be embedded in Rpt. In addition to lattice theoretic representation theorems, they use ... View full abstract»

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  • The power of parallel random access machines with augmented instruction sets

    Publication Year: 1989, Page(s):97 - 103
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (592 KB)

    It is proved that the class of languages accepted in polynomial time by a parallel random access machine (PRAM) with both multiplication and shifts contains NEXPTIME and is contained in EXPSPACE. Thus, such a PRAM may be more powerful, to within a polynomial in time, that one with either multiplication or shifts alone. Bounds are established on the simulation of PRAMs with augmented instruction se... View full abstract»

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  • p-creative sets vs. p-completely creative sets

    Publication Year: 1989, Page(s):24 - 33
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (800 KB)

    It is shown that for recursively enumerable sets, p-creativeness and p-complete creativeness are equivalent, and Myhill's theorem still holds in the polynomial setting. For P (NP), p-creativeness is shown to be equivalent to p-complete creativeness. The existence of p-creative sets for P (NP) in EXP (NEXP) is given. Moreover, it is shown that every p-m-complete set for EXP (NEXP) is p-completely c... View full abstract»

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  • Nondeterministic witnesses and nonuniform advice

    Publication Year: 1989, Page(s):259 - 269
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (936 KB)

    Several results related to nonuniform complexity classes and their comparison with uniform ones are surveyed. The relevance of the main tools in these arguments, namely, self-reducibility structures is explained by showing that the methods for proving relationships between nonuniform and uniform classes, including the so-called round-robin tournament method, can be presented as general properties ... View full abstract»

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  • Decomposing NC and AC

    Publication Year: 1989, Page(s):124 - 131
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    It is shown that it is possible to decompose any level of NC into components involving lower levels. The results are extended to the class AC. The method presented results in a natural way to provide NC and AC with oracles View full abstract»

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  • On honest polynomial reductions, relativizations, and P=NP

    Publication Year: 1989, Page(s):196 - 207
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (844 KB)

    The authors prove a number of structural theorems about the honest polynomial m-degrees, contingent on the assumption P=NP (or a unary alphabet). The ultimate goal would be to prove a contradiction from P=NP. They show that low sets cannot be minimal with respect. They also show that some theorems about honest polynomial reductions do not relativize; hence, techniques in this area may be ... View full abstract»

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  • The complexity of the real line is a fractal

    Publication Year: 1989, Page(s):138 - 146
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (440 KB)

    The authors investigate the Kolmogorov complexity of real numbers. They determine the Hausdorff dimension and the topological dimension of the graph of K, the Kolmogorov complexity function. They conclude that the complexity graph is a fractal View full abstract»

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  • On the power of probabilistic polynomial time: PNP[log] ⊆ PP

    Publication Year: 1989, Page(s):225 - 227
    Cited by:  Papers (5)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (156 KB)

    It is shown that probabilistic time is closed under polynomial-time parity reductions. Therefore, every set polynomial-time truth-table reducible to SAT is accepted by a probabilistic polynomial-time Turing machine. Equivalently, PNP[log] ⊆ PP View full abstract»

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  • Composition is almost as good as s-1-1

    Publication Year: 1989, Page(s):77 - 86
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (816 KB)

    The author establishes a polynomial upper bound on the time complexity of s-1-1 in programming systems with a linear time instance of composition. He also exhibits a family of acceptable such programming systems for which the upper bound is optimal. He deduces several bounds on the time complexity of composition, s-1-1, and various classes of control structures in effective or ar... View full abstract»

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