and logic, and much progress has been made in developing verification algorithms, heuristics, and tools. This paper provides a survey of the theory of timed automata, and their role in specification and verification of real-time systems.

A hybrid automaton is a formal model for a mixed discrete-continuous system. We classify hybrid automata acoording to what questions about their behavior can be answered algorithmically. The classification reveals structure on mixed discrete-continuous state spaces that was previously studied

Conventional type systems specify interfaces in terms of values and domains.

We introduce the framework of hybrid automata as a model and specification language for hybrid systems. Hybrid automata can be viewed as a generalization of timed automata, in which the behavior of variables is governed in each state by a set of differential equations. We show that many

We give an efficient procedure for verifying that a finite-state concurrent system meets a specification expressed in a (propositional, branching-time) temporal logic. Our algorithm has complexity linear in both the size of the specification and the size of the global state graph for the concurrent

then introduce a new search technique that is suitable for exploring the state spaces of such systems. This algorithm has been implemented in VeriSoft, a tool for systematically exploring the state spaces of systems composed of several concurrent processes executing arbitrary C code. As an example of application

We describe finite-state programs over real-numbered time in a guarded-command language with real-valued clocks or, equivalently, as finite automata with real-valued clocks. Model checking answers the question which states of a real-time program satisfy a branching-time specification (given

We present a new tool, named DART, for automatically testing software that combines three main techniques: (1) automated extraction of the interface of a program with its external environment using static source-code parsing; (2) automatic generation of a test driver for this interface

), and difficult to optimize (which is necessary to combat the exponential complexity of verification algorithms). In this paper, we describe an integrated collection of program analysis and transformation components, called Bandera, that enables the automatic extraction of safe, compact finite-state models from

We develop techniques to compute higher loop string amplitudes for twisted N = 2 theories with ĉ = 3 (i.e. the critical case). An important ingredient is the discovery of an anomaly at every genus in decoupling of BRST trivial states, captured to all orders by a master anomaly equation. In a