Conference Paper
Generation Complexity Versus Distinction Complexity.
DOI: 10.1007/9783540792284_40
Conference: Theory and Applications of Models of Computation, 5th International Conference, TAMC 2008, Xi'an, China, April 2529, 2008. Proceedings
Source: DBLP
 Citations (5)

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Article: Randomness conservation inequalities; information and independence in mathematical theories
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ABSTRACT: The article further develops Kolmogorov's algorithmic complexity theory. The definition of randomness is modified to satisfy strong invariance properties (conservation inequalities). This allows definitions of concepts such as mutual information in individual infinite sequences. Applications to several areas, like probability theory, theory of algorithms, intuitionistic logic are considered. These theories are simplified substantially with the postulate that the objects they consider are independent of (have small mutual information with) any sequence specified by a mathematical property.Information and Control 04/1984; DOI:10.1016/S00199958(84)800601 
Conference Paper: A Complexity Theoretic Approach to Randomness
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ABSTRACT: We study a time bounded variant of Kolmogorov complexity. This notion, together with universal hashing, can be used to show that problems solvable probabilistically in polynomial time are all within the second level of the polynomial time hierarchy. We also discuss applications to the theory of probabilistic constructions.Proceedings of the 15th Annual ACM Symposium on Theory of Computing, 2527 April, 1983, Boston, Massachusetts, USA; 01/1983 
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ABSTRACT: This paper studies the power of access, especially faulttolerant access, to probabilistic databases and to unambiguous databases. We study faulttolerant access to probabilistic computation, and completely characterize the complexity classes R and ZPP in terms of faulttolerant database access. We also show that consistent and inconsistent failure are in general interchangeable. We study the power of three types of access to unambiguous computation: nonadaptive access, faulttolerant access, and guarded access. (1) Though for NP it is known that nonadaptive access has exponentially terse adaptive simulations, we show that UP has no such relativizable simulations: there are worlds in which k+1truthtable access to UP is not subsumed by kTuring access to UP, or even to NP machines that are unambiguous on the questions actually asked. (2) Though faulttolerant access (i.e., ``1helping'' access) to NP is known to be no more powerful than NP itself, we give both structural and relativized evidence that fault tolerant access to UP suffices to recognize even sets beyond UP. Furthermore, we completely characterize, in terms of locally positive reductions, the sets that faulttolerantly reduce to UP. (3) In guarded access, Grollmann and Selman's natural notion of access to unambiguous computation, a deterministic polynomialtime Turing machine asks questions to a nondeterministic polynomialtime Turing machine in such a way that the nondeterministic machine never accepts ambiguously. In contrast to guarded access, the standard notion of access to unambiguous computation is that of access to a set that is uniformly unambiguouseven for queries that it never will be asked by its questioner, it must be unambiguous. We show that these notions, though the same for nonadaptive reductions, differ for Turing and strong nondeterministic reductions.
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