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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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Book
01 Jan 1988
TL;DR: The notion of regular rewriting systems is defined, and cost series associated with operators that are described by such systems are considered, and analysis methods apply to compute such costs and provide an asymptotic evaluation of the average cost of an operator.
Abstract: Algebraic specifications are now widely used for data structuring and they turn out to be quite useful for various aspects of program development, such as prototyping, assisted program construction, proving properties, etc [3, 12, 13, 15, 16, 17, 181 Some of these applications require adding a notion of computation to algebraic specifications, for instance by providing a (convergent) rewrite rule system that expresses the properties of the operators In this context, it may be of prime interest to define a notion of algorithmic complexity for an algebraic specification, or, more precisely, a notion of complexity for each operator defined in the specification Computing operator complexity within a given specification helps understanding how evaluation costs are distributed; it may single out “costly” operators, and motivate the search for an equivalent, but “cheaper”, specification In [5], the cost of a term is defined as the number of rewriting steps for reducing it to its normal form, and the cost of an operator is defined as the genera1 cost of a term obtained by applying this operator to terms in normal form In this paper, we further formalize this notion of operator complexity and investigate its computation through analysis methods developed for instance in [24,9] We show how these methods apply to the computation of the enumerative series related to the terms of an algebraic specification We define the notion of regular rewriting systems, and consider cost series associated with operators that are described by such systems We show how these analysis methods apply to compute such costs and provide an asymptotic evaluation of the average cost of an operator Our results allow costs to be computed without any explicit manipulation of series We provide the user with ready-to-use formulae, where the different parameters only depend on the “geometry” of the system, eg the number of constructors in the left-hand side of rules, number of occurrences of a derived operator in the right-hand side, etc Quantitative evaluation of rewriting systems had not yet been studied under such an approach (except in [5]), to our knowledge From a different point of view, complexity of algebraic implementations has been studied in [2,8 etc] wrt computability issues

36 citations

Journal ArticleDOI
01 Jan 2012
TL;DR: It is proved that for every computable measurable space, RN is W-reducible to EC, and a computable measured space is constructed for which EC isW-reduced to RN.
Abstract: We show that a single application of the noncomputable operator EC, which transforms enumerations of sets (in N) to their characteristic functions, suffices to compute the Radon-Nikodym derivative dµ/dλ of a finite measure µ, which is absolutely continuous w.r.t. the σ-finite measure λ. We also give a condition on the two measures (in terms of computability of the norm of a certain linear operator involving the two measures) which is sufficient to compute the derivative.

36 citations

Proceedings Article
01 Jan 2014
TL;DR: This paper removes the assumption that three collinear robots are mutually visible, and presents an algorithm that solves Mutual Visibility, and solves a seemingly unrelated problem, Communicating Vessels, which is interesting in its own right.
Abstract: Consider a nite set of identical entities, called robots, which can move freely in the Euclidean plane. Let p(t) denote the location of robot p at time t; a robot p can see robot q at time t if at that time no other robot lies in the line segment p(t)q(t). We consider the basic problem called Mutual Visibility: starting from arbitrary distinct locations, within nite time the robots must reach, without collisions, a conguration where they all see each other. This problem must be solved by each entity autonomously executing the same algorithm. We study this problem in the standard model of semi-synchronous oblivious robots. The extensive literature on computability in such a model has never considered this problem because it has always assumed that three collinear robots are mutually visible. In this paper we remove this assumption, and present an algorithm that solves Mutual Visibility. To prove its correctness, we solve a seemingly unrelated problem, Communicating Vessels, which is interesting in its own right. As a byproduct of our solution, we also solve a classical problem for oblivious robots, Near-Gathering, even if one robot is faulty and unable to move.

36 citations

Proceedings ArticleDOI
26 Sep 2013
TL;DR: This work proposes a novel algorithm for the satisfiability problem for Linear Temporal Logic that works on-the-fly by inspecting the formula directly, thus enabling finding a satisfying model quickly without constructing the full automaton.
Abstract: We propose a novel algorithm for the satisfiability problem for Linear Temporal Logic (LTL). Existing approaches first transform the LTL formula into a B"uchi automaton and then perform an emptiness checking of the resulting automaton. Instead, our approach works on-the-fly by inspecting the formula directly, thus enabling finding a satisfying model quickly without constructing the full automaton. This makes our algorithm particularly fast for satisfiable formulas. We report on a prototype implementation, showing that our approach significantly outperforms state-of-the-art tools.

36 citations

Book
01 Jan 1965

36 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202344
2022119
202189
202098
2019111
201897