Topic
Average-case complexity
About: Average-case complexity is a research topic. Over the lifetime, 1749 publications have been published within this topic receiving 44972 citations.
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TL;DR: This paper relies on the classical work by Gentzen Ge 36], Kreisel Kr 52] and Wainer Wa 72].
Abstract: Long regressive sequences in well-quasi-ordered sets contain ascendingsubsequences of length n. The complexity of the corresponding function H(n) is studied in the Grzegorczyk-Wainer hierarchy. An extension to regressive canonical colourings is indicated.
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TL;DR: This paper extends some of the results related to the comparison of one-variable complexity functions using complexity classes to multivariable complexity functions.
Abstract: The comparison of algorithms complexities can be r educed to the comparison of complexity functions. In two previous papers, we obtained some results related to the comparison of one-variable complexity functions usi ng complexity classes. In this paper, we extend some of these results to multivariable co mplexity functions.
15 Jan 2006
TL;DR: The theory of real-valued computation and complexity deals with foundational aspects of scientific computation and a computational model whose basic unity of information is a real number reasonably captures this feature.
Abstract: The theory of real-valued computation and complexity deals with foundational aspects of scientific computation. Here the basic unit of information is the floating-point number and a computational model whose basic unity of information is a real number reasonably captures this feature.
Keywords:
real complexity;
NP-completeness;
equation solving
17 Jun 1996
TL;DR: In this article, simple stochastic games (SSGs) under uncertainty were investigated and the computational complexity of deciding whether a given SSG is stopping (discounted) or not was investigated.
Abstract: We investigate simple stochastic games (SSGs): a kind of two-person games under uncertainty, the original model of which was introduced in [L.S. Shapley, Proc. Nat. Acad. Sci. U.S.A.39 (1953) 1095–1100]. We consider the computational complexity of
1.
deciding whether a given SSG is stopping (discounted) or not,
2.
counting the number of all the optimal strategies of SSGs,
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finding an optimal strategy against the player who takes random strategies.
TL;DR: A new approach to defining complexity of propositional formulas and proofs is suggested to define the complexity by the size of external descriptions of such constructions, resulting in a lower bound on proof complexity.
Abstract: A new approach to defining complexity of propositional formulas and proofs is suggested. Instead of measuring the size of these syntactical structures in the propositional language, the article suggests to define the complexity by the size of external descriptions of such constructions. The main result is a lower bound on proof complexity with respect to this new definition of complexity.