Speciication and Veriication of Constraint-based Dynamic Systems 1 Motivation and Introduction

Constraint satisfaction can be seen as a dynamic process that approaches the solution set of the given constraints asymptotically 6]. Constraint programming is seen as creating a dynamic system with the required property. We have developed a semantic model for dynamic systems, Constraint Nets, which serves as a useful abstract target machine for constraint programming languages, providing both semantics and pragmatics. Generalizing, here we view a constraint-based dynamic system as a dynamic system which approaches the solution set of the given constraints persistently. Most robotic systems are constraint-based dynamic systems with tasks speciied as constraints. In this paper, we further explore the speciication and veriication of constraint-based dynamic systems. We rst develop generalized 8-automata for the speciica-tion and veriication of general (hybrid) dynamic systems, then explicate the relationship between constraint-based dynamic systems and their requirements speciication. We have previously proposed viewing constraints as relations and constraint satisfaction as a dynamic process of approaching the solution set of the constraints asymptotically 6]. Under this view, constraint programming is the creation of a dynamic system with the required property. We have developed a semantic model for dynamic systems, Constraint Nets, which serves as a useful abstract target machine for constraint programming languages, providing both semantics and pragmatics. Properties of various discrete and continuous constraint methods for constraint programming have also been examined 6]. Generalizing, here we consider a constraint-based dynamic system as a dynamic system which approaches the solution set of the given constraints persistently. One of the motivations for this view is to design and analyze a robotic system composed of a controller that is coupled to a plant and an environment.