Computability

About: Computability is a research topic. Over the lifetime, 2829 publications have been published within this topic receiving 85162 citations.

Symbolic models for time-varying time-delay systems via alternating approximate bisimulation

Abstract: Summary Time-delay systems are an important class of dynamical systems that provide a solid mathematical framework to deal with many application domains of interest. In this paper, we focus on nonlinear control systems with unknown and time-varying delay signals and we propose one approach to the control design of such systems, which is based on the construction of symbolic models. Symbolic models are abstract descriptions of dynamical systems where one symbolic state and one symbolic input correspond to an aggregate of states and an aggregate of inputs. We first introduce the notion of incremental input-delay-to-state stability and provide sufficient conditions to check it in terms of existence of Lyapunov–Krasovskii functionals. We then derive sufficient conditions for the existence of symbolic models that are shown to be alternating approximately bisimilar to the original system. Further results are also derived, which prove the computability of the proposed symbolic models in a finite number of steps. Copyright © 2014 John Wiley & Sons, Ltd.

Enhancing dependency pair method using strong computability in simply-typed term rewriting

Abstract: We enhance the dependency pair method in order to prove termination using recursive structure analysis in simply-typed term rewriting systems, which is one of the computational models of functional programs. The primary advantage of our method is that one can exclude higher-order variables which are difficult to analyze theoretically, from recursive structure analysis. The key idea of our method is to analyze recursive structure from the viewpoint of strong computability. This property was introduced for proving termination in typed λ-calculus, and is a stronger condition than the property of termination. The difficulty in incorporating this concept into recursive structure analysis is that because it is defined inductively over type structure, it is not closed under the subterm relation. This breaks the correspondence between strong computability and recursive structure. In order to guarantee the correspondence, we propose plain function-passing as a restriction, which is satisfied by many non-artificial functional programs.

Revisiting the Decomposition of Karp, Miller and Winograd

Abstract: This paper is devoted to the construction of multi-dimensional schedules for a system of uniform recurrence equations. We show that this problem is dual to the problem of computability of a system of uniform recurrence equations. We propose a new study of the decomposition algorithm first proposed by Karp, Miller and Winograd: we base our implementation on linear programming resolutions whose duals give exactly the desired multi-dimensional schedules. Furthermore, we prove that the schedules built this way are optimal up to a constant factor.