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Computability
About: Computability is a research topic. Over the lifetime, 2829 publications have been published within this topic receiving 85162 citations.
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TL;DR: This paper proposes a refinement of the real-number model of computation with the condition “every partial input or output information of an algorithm is finite” to the assumptions of the IBC-model of computation, and explains computability and computational complexity in TTE for the simple case of real functions.
9 citations
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TL;DR: An efficient formalism inspired by algorithms to define long sequences of updates that allows a better description of the transient and asymptotic dynamics of asynchronous Boolean automata networks composed of two cycles that intersect at one automaton, the so-called double-cycles are introduced.
Abstract: The understanding of Boolean automata networks dynamics takes an important place in various domains of computer science such as computability, complexity and discrete dynamical systems In this paper, we make a step further in this understanding by focusing on their cycles, whose necessity in networks is known as the brick of their complexity We present new results that provide a characterisation of the transient and asymptotic dynamics, ie of the computational abilities, of asynchronous Boolean automata networks composed of two cycles that intersect at one automaton, the so-called double-cycles To do so, we introduce an efficient formalism inspired by algorithms to define long sequences of updates, that allows a better description of their dynamics than previous works in this area
9 citations
TL;DR: For such W -functions the concepts of (‘crisp’) computability and recursiveness are extended, obtaining the so called W -computability and W -recursiveness respectively.
9 citations
15 Jun 1998
TL;DR: In this article, the complexity and the efficient approximability of graph and satisfiability problems when specified using various kinds of periodic specifications studied previously were studied. But the complexity of SAT(S) was not characterized.
Abstract: We study the complexity and the efficient approximability of graph and satisfiability problems when specified using various kinds of periodic specifications studied previously. We obtain two general results. First, we characterize the complexities of several basic generalized CNF satisfiability problems SAT(S), when instances are specified using various kinds of 1- and 2-dimensional periodic specifications. We outline how this characterization can be used to prove a number of new hardness results for periodically specified problems for various complexity classes. As one corollary, we show that a number of basic NP-hard problems become EXPSPACE-hard when inputs are represented using 1-dimensional infinite periodic wide specifications, thereby answering an open question. Second, we outline a simple yet a general technique to devise approximation algorithms with provable worst case performance guarantees for a number of combinatorial problems specified periodically. Our efficient approximation algorithms and schemes are based on extensions of the previous ideas. They provide the first nontrivial collection of natural NEXPTIME-hard problems that have an /spl epsiv/-approximation (or PTAS).
9 citations