Topic
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: In this article, the authors show that any open subset of a self-similar set with open set condition may be tiled without loss of measure by copies under similitudes of any closed subset with positive measure.
Abstract: We state a self-similar tiling principle which shows that any open subset of a self-similar set with open set condition may be tiled without loss of measure by copies under similitudes of any closed subset with positive measure. We use this method to get the optimal coverings and packings which give the exact value of the Hausdorff-type and packing measures. In particular, we show that the exact value of these measures coincides with the supremum or with the infimum of the inverse of the density of the natural probability measure on suitable classes of sets. This gives criteria for the numerical analysis of the measures, and allows us to compare their complexity in terms of computability.
22 citations
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TL;DR: In this article, the authors consider reachability games over general hybrid systems, and distinguish between two possible observation frameworks for those games: either the precise dynamics of the system is seen by the players (this is the perfect observation framework), or only the starting point and the delays are known to the players, this is the partial observation framework.
Abstract: In this paper, we consider reachability games over general hybrid systems,
and distinguish between two possible observation frameworks for those games:
either the precise dynamics of the system is seen by the players (this is the
perfect observation framework), or only the starting point and the delays are
known by the players (this is the partial observation framework). In the first
more classical framework, we show that time-abstract bisimulation is not
adequate for solving this problem, although it is sufficient in the case of
timed automata . That is why we consider an other equivalence, namely the
suffix equivalence based on the encoding of trajectories through words. We show
that this suffix equivalence is in general a correct abstraction for games. We
apply this result to o-minimal hybrid systems, and get decidability and
computability results in this framework. For the second framework which assumes
a partial observation of the dynamics of the system, we propose another
abstraction, called the superword encoding, which is suitable to solve the
games under that assumption. In that framework, we also provide decidability
and computability results.
22 citations
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23 Nov 2009
TL;DR: This work provides an operational semantics for self-modification programs and it is shown that they can be constructively rewritten to a non-modifying program.
Abstract: In order to increase their stealth, malware commonly use the self-modification property of programs. By doing so, programs can hide their real code so that it is difficult to define a signature for it. But then, what is the meaning of those programs: the obfuscated form, or the hidden one? Furthermore, from a computability perspective, it becomes hard to speak about the program since, its own code varies over time. To cope with these issues, we provide an operational semantics for self-modifying programs and we show that they can be constructively rewritten to a non-modifying program.
22 citations
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08 Apr 1987TL;DR: N. N. Saheb-Sjahromi's probabilistic domain construction is extended to non-algebraic domains, particularly RSFP objects and the construction is shown to be free.
Abstract: Various closure properties of a domain theoretic construction for a probabilistic domain are considered N Saheb-Sjahromi's probabilistic domain construction is extended to non-algebraic domains, particularly RSFP objects An abstract notion of a probabilistic domain is presented and the construction is shown to be free Issues of computability and approaches to solving domain equations in probabilistic domains are addressed briefly
22 citations
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TL;DR: In this paper, a certain phenomenon of consciousness is demonstrated to be fully represented as a computational process using a quantum computer, based on the computability criterion discussed with Turing machines, the model constructed is shown to necessarily involve a non-computable element.
Abstract: With the great success in simulating many intelligent behaviors using computing devices, there has been an ongoing debate whether all conscious activities are computational processes. In this paper, the answer to this question is shown to be no. A certain phenomenon of consciousness is demonstrated to be fully represented as a computational process using a quantum computer. Based on the computability criterion discussed with Turing machines, the model constructed is shown to necessarily involve a non-computable element. The concept that this is solely a quantum effect and does not work for a classical case is also discussed.
22 citations