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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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06 Jun 2005
TL;DR: This work first shows the Turing-computability of the problem of computing the shortest obstacle-avoiding path between two points p, q in the plane, and shows single-exponential time upper bound when the input numbers are rational.
Abstract: An open question in Exact Geometric Computation is whether there re transcendental computations that can be made "geometrically exact".Perhaps the simplest such problem in computational geometry is that of computing the shortest obstacle-avoiding path between two points p, q in the plane, where the obstacles re collection of n discs.This problem can be solved in O (n 2 log n)time in the Real RAM model, but nothing was known about its computability in the standard (Turing) model of computation. We first show the Turing-computability of this problem,provided the radii of the discs are rationally related. We make the usual assumption that the numerical input data are real algebraic numbers. By appealing to effective bounds from transcendental number theory, we further show single-exponential time upper bound when the input numbers are rational.Our result ppears to be the first example of non-algebraic combinatorial problem which is shown computable. It is also rare example of transcendental number theory yielding positive computational results.
23 citations
TL;DR: This work generalizes the following two language- and automata-theoretic results to ω-continuous semirings and concludes that the family of languages accepted by pushdown automata is thefamily of context-free languages.
23 citations
28 May 2008
TL;DR: The techniques underlying SMT are overviewed, it is shown how to represent dynamic systems in fragments of first order logic, and the application of SMT solvers to their verification is discussed.
Abstract: Many systems can be naturally represented in some decidable fragments of first order logic. The expressive power provided by a background theory allows to describe important aspects such as real time, continuous dynamics, and data flow over integer variables. The corresponding verification problems can be tackled by means of Satisfiability Modulo Theory (SMT) solvers. SMT solvers are based on the tight integration of propositional SAT solvers with dedicated procedures to reason about the theory component. In this paper, we overview the techniques underlying SMT, we show how to represent dynamic systems in fragments of first order logic, and discuss the application of SMT solvers to their verification.
23 citations
TL;DR: A verification framework for implicit invocation is developed based on Jones' rely/guarantee reasoning for concurrent systems [Jon83, Stø91], and the application of the framework is illustrated with several examples.
Abstract: Implicit invocation [SuN92, GaN91] has become an important architectural style for large-scale system design and evolution. This paper addresses the lack of specification and verification formalisms for such systems. A formal computational model for implicit invocation is presented. We develop a verification framework for implicit invocation that is based on Jones' rely/guarantee reasoning for concurrent systems [Jon83, StO91]. The application of the framework is illustrated with several examples. The merits and limitations of the rely/guarantee paradigm in the context of implicit invocation systems are also discussed.
23 citations
Journal Article•
23 citations