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The algorithmic analysis of hybrid systems
 THEORETICAL COMPUTER SCIENCE
, 1995
"... We present a general framework for the formal specification and algorithmic analysis of hybrid systems. A hybrid system consists of a discrete program with an analog environment. We model hybrid systems as nite automata equipped with variables that evolve continuously with time according to dynamica ..."
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Cited by 596 (69 self)
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We present a general framework for the formal specification and algorithmic analysis of hybrid systems. A hybrid system consists of a discrete program with an analog environment. We model hybrid systems as nite automata equipped with variables that evolve continuously with time according to dynamical laws. For verification purposes, we restrict ourselves to linear hybrid systems, where all variables follow piecewiselinear trajectories. We provide decidability and undecidability results for classes of linear hybrid systems, and we show that standard programanalysis techniques can be adapted to linear hybrid systems. In particular, we consider symbolic modelchecking and minimization procedures that are based on the reachability analysis of an infinite state space. The procedures iteratively compute state sets that are definable as unions of convex polyhedra in multidimensional real space. We also present approximation techniques for dealing with systems for which the iterative procedures do not converge.
Hybrid Automata: An Algorithmic Approach to the Specification and Verification of Hybrid Systems
, 1992
"... 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 of the examp ..."
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Cited by 360 (20 self)
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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 of the examples considered in the workshop can be defined by hybrid automata. While the reachability problem is undecidable even for very restricted classes of hybrid automata, we present two semidecision procedures for verifying safety properties of piecewiselinear hybrid automata, in which all variables change at constant rates. The two procedures are based, respectively, on minimizing and computing fixpoints on generally infinite state spaces. We show that if the procedures terminate, then they give correct answers. We then demonstrate that for many of the typical workshop examples, the procedures do terminate and thus provide an automatic way for verifying their properties. 1 Introduction More and...
From Timed to Hybrid Systems
"... We propose a framework for the formal speci cation and veri cation of timed and hybrid systems. For timed systems we propose a speci cation language that refers to time only through age functions which measure the length of the most recent timeinterval in which agiven formula has been continuously t ..."
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Cited by 146 (16 self)
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We propose a framework for the formal speci cation and veri cation of timed and hybrid systems. For timed systems we propose a speci cation language that refers to time only through age functions which measure the length of the most recent timeinterval in which agiven formula has been continuously true. We then consider hybrid systems, which are systems consisting of a nontrivial mixture of discrete and continuous components, such as a digital controller that controls acontinuous environment. The proposed framework extends the temporal logic approach which has proven useful for the formal analysis of discrete systems such as reactive programs. The new framework consists of a semantic model for hybrid time, the notion of phase transition systems, which extends the formalism of discrete transition systems, an extended version of Statecharts for the speci cation of hybrid behaviors, and an extended version of temporal logic that enables reasoning about continuous change.
An Approach to the Description and Analysis of Hybrid Systems
"... Introduction The paper presents a model for hybrid systems, that is, systems that combine discrete and continuous components. Such systems are usually reactive realtime systems used to control an environment evolving over time. A main assumption is that a run of a hybrid system is a sequence of two ..."
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Cited by 77 (3 self)
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Introduction The paper presents a model for hybrid systems, that is, systems that combine discrete and continuous components. Such systems are usually reactive realtime systems used to control an environment evolving over time. A main assumption is that a run of a hybrid system is a sequence of twophase steps. The first phase of a step corresponds to a continuous state transformation usually described in terms of some parameter representing the time elapsed during this phase. In the second phase the state is submitted to a discrete change taking zero time. To illustrate this assumption, consider a temperature regulator commanding a heater so as to maintain the temperature ` of a room between two given bounds ` min and ` max . A run of such a system is a sequence of steps determined by the alternating state changes of the heater from ON to OFF<F26.
Compiling RealTime Specifications into Extended Automata
 IEEE Transactions on Software Engineering
, 1992
"... We propose a method for the implementation and analysis of realtime systems, based on the compilation of specifications into extended automata. Such a method has been already adopted for the so called "synchronous" realtime programming languages. ..."
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Cited by 75 (8 self)
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We propose a method for the implementation and analysis of realtime systems, based on the compilation of specifications into extended automata. Such a method has been already adopted for the so called "synchronous" realtime programming languages.
Integration Graphs: A Class of Decidable Hybrid Systems
 In Hybrid Systems, volume 736 of Lecture Notes in Computer Science
, 1993
"... . Integration Graphs are a computational model developed in the attempt to identify simple Hybrid Systems with decidable analysis problems. We start with the class of constant slope hybrid systems (cshs), in which the right hand side of all differential equations is an integer constant. We refer to ..."
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Cited by 67 (9 self)
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. Integration Graphs are a computational model developed in the attempt to identify simple Hybrid Systems with decidable analysis problems. We start with the class of constant slope hybrid systems (cshs), in which the right hand side of all differential equations is an integer constant. We refer to continuous variables whose right hand side constants are always 1 as timers. All other continuous variables are called integrators. The first result shown in the paper is that simple questions such as reachability of a given state are undecidable for even this simple class of systems. To restrict the model even further, we impose the requirement that no test that refers to integrators may appear within a loop in the graph. This restricted class of cshs is called integration graphs . The main results of the paper are that the reachability problem of integration graphs is decidable for two special cases: The case of a single timer and the case of a single test involving integrators. The expres...
Forward and backward simulations for timingbased systems
 In de Bakker et al
, 1991
"... A general automaton model for timingbased systems is presented and is used as the context for developing a variety of simulation proof techniques for such systems. As a first step, a comprehensive overview of simulation techniques for simple untimed automata is given. In particular, soundness and ..."
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Cited by 63 (16 self)
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A general automaton model for timingbased systems is presented and is used as the context for developing a variety of simulation proof techniques for such systems. As a first step, a comprehensive overview of simulation techniques for simple untimed automata is given. In particular, soundness and completeness results for (1) refinements, (2) forward and backward simulations, (3) forwardbackward and backwardforward simulations, and (4) history and prophecy relations are given. History and prophecy relations are new and are abstractions of the history variables of Owicki and Gries and the prophecy variables of Abadi and Lamport, respectively. As a subsequent step, it is shown how most of the results for untimed automata can be carried over to the setting of timed automata. In fact, many of the results for the timed case are obtained as consequences of the analogous results for the untimed case.
Verifying ETLOTOS programs with KRONOS
 In Proc. FORTE'94
, 1994
"... This paper shows that realtime systems described in a reasonable subset of ETLOTOS can be verified with Kronos by compiling them into timed automata. We illustrate the practical interest of our approach with a case study: the TickTock protocol ..."
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Cited by 48 (9 self)
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This paper shows that realtime systems described in a reasonable subset of ETLOTOS can be verified with Kronos by compiling them into timed automata. We illustrate the practical interest of our approach with a case study: the TickTock protocol
Automatic Verification of RealTime Communicating Systems by ConstraintSolving
 In Proc. of the 7th International Conference on Formal Description Techniques
, 1994
"... this paper, an algebra of timed processes with realvalued clocks is presented, which serves as a formal description language for realtime communicating systems. We show that requirements such as "a process will never reach an undesired state" can be verified by solving a simple class of constrai ..."
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Cited by 43 (15 self)
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this paper, an algebra of timed processes with realvalued clocks is presented, which serves as a formal description language for realtime communicating systems. We show that requirements such as "a process will never reach an undesired state" can be verified by solving a simple class of constraint systems on the clockvariables. A complete method for reachability analysis associated with the language is developed, and implemented as an automatic verification tool based on constraintsolving techniques. Finally as examples, we study and verify the safetyproperties of Fischer's mutual exclusion protocol and a railway crossing controller.