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Timed automata: Semantics, algorithms and tools
 Lectures on Concurrency and Petri Nets: Advances in Petri Nets, number 3098 in LNCS
, 2004
"... Abstract. This chapter is to provide a tutorial and pointers to results and related work on timed automata with a focus on semantical and algorithmic aspects of verification tools. We present the concrete and abstract semantics of timed automata (based on transition rules, regions and zones), decisi ..."
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Cited by 171 (4 self)
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Abstract. This chapter is to provide a tutorial and pointers to results and related work on timed automata with a focus on semantical and algorithmic aspects of verification tools. We present the concrete and abstract semantics of timed automata (based on transition rules, regions and zones), decision problems, and algorithms for verification. A detailed description on DBM (Difference Bound Matrices) is included, which is the central data structure behind several verification tools for timed systems. As an example, we give a brief introduction to the tool UPPAAL. 1
Hybrid I/O Automata
, 1996
"... Hybrid systems are systems that exhibit a combination of discrete and continuous behavior. Typical hybrid systems include computer components, which operate in discrete program steps, and realworld components, whose behavior over time intervals evolves according to physical constraints. Important e ..."
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Cited by 170 (23 self)
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Hybrid systems are systems that exhibit a combination of discrete and continuous behavior. Typical hybrid systems include computer components, which operate in discrete program steps, and realworld components, whose behavior over time intervals evolves according to physical constraints. Important examples of hybrid systems include automated transportation systems, robotics systems, process control systems, systems of embedded devices, and mobile computing systems. Such systems can be very complex, and very dicult to describe and analyze.
A user guide to HYTECH
, 1995
"... HyTech is a tool for the automated analysis of embedded systems. This document, designed for the rsttime user of HyTech, guides the reader through the underlying system model, and through the input language for describing and analyzing systems. The guide gives installation instructions, several exa ..."
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Cited by 158 (4 self)
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HyTech is a tool for the automated analysis of embedded systems. This document, designed for the rsttime user of HyTech, guides the reader through the underlying system model, and through the input language for describing and analyzing systems. The guide gives installation instructions, several examples of usage, some hints for gaining maximal computational e ciency from the tool, and the complete grammar for the input language. This guide describes version 1.04 of HyTech. The latest update occurred in October 1996 1. HyTech is available through the WorldWide Web at
CONTROLLER SYNTHESIS FOR TIMED AUTOMATA
"... In this work we tackle the following problem: given a timed automaton, restrict its transition relation in a systematic way so that all the remaining behaviors satisfy certain properties. This is an extension of the problem of controller synthesis for discrete event dynamical systems, where in addi ..."
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Cited by 157 (14 self)
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In this work we tackle the following problem: given a timed automaton, restrict its transition relation in a systematic way so that all the remaining behaviors satisfy certain properties. This is an extension of the problem of controller synthesis for discrete event dynamical systems, where in addition to choosing among actions, the controller have the option of doing nothing and let the time pass. The problem is formulated using the notion of a realtime game, and a winning strategy is constructed as a fixedpoint of an operator on the space of states and clock configurations.
Kronos: A modelchecking tool for realtime systems,” in Computer Aided Verification, ser.
 Lecture Notes in Computer Science, A. Hu
, 1998
"... ..."
Approximate Reachability Analysis of PiecewiseLinear Dynamical Systems
, 2000
"... . In this paper we describe an experimental system called d=dt for approximating reachable states for hybrid systems whose continuous dynamics is defined by linear differential equations. We use an approximation algorithm whose accumulation of errors during the continuous evolution is much small ..."
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Cited by 140 (31 self)
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. In this paper we describe an experimental system called d=dt for approximating reachable states for hybrid systems whose continuous dynamics is defined by linear differential equations. We use an approximation algorithm whose accumulation of errors during the continuous evolution is much smaller than in previouslyused methods. The d=dt system can, so far, treat nontrivial continuous systems, hybrid systems, convex differential inclusions and controller synthesis problems. 1 Introduction The problem of calculating reachable states for continuous and hybrid systems has emerged as one of the major problems in hybrid systems research [G96,GM98,DM98,KV97,V98,GM99,CK99,PSK99,HHMW99]. It constitutes a prerequisite for exporting algorithmic verification methodology outside discrete systems or hybrid systems with piecewisetrivial dynamics. For computer scientists it poses new challenges in treating continuous functions and their approximations and in applying computational geometry...
Algorithmic analysis of nonlinear hybrid systems
 in Proc. CAV 95: Computeraided Verification, Lecture Notes in Computer Science
, 1995
"... Abstract—Hybrid systems are digital realtime systems that are embedded in analog environments. Modelchecking tools are available for the automatic analysis of linear hybrid automata, whose environment variables are subject to piecewiseconstant polyhedral differential inclusions. In most embedded ..."
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Cited by 138 (13 self)
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Abstract—Hybrid systems are digital realtime systems that are embedded in analog environments. Modelchecking tools are available for the automatic analysis of linear hybrid automata, whose environment variables are subject to piecewiseconstant polyhedral differential inclusions. In most embedded systems, however, the environment variables have differential inclusions that vary with the values of the variables, e.g., _x = x. Such inclusions are prohibited in the linear hybrid automaton model. We present two methods for translating nonlinear hybrid systems into linear hybrid automata. Properties of the nonlinear systems can then be inferred from the automatic analysis of the translated linear hybrid automata. The first method, called clock translation, replaces constraints on nonlinear variables by constraints on clock variables. The clock translation is efficient but has limited applicability. The second method, called linear phaseportrait approximation, conservatively overapproximates the phase portrait of a hybrid automaton using piecewiseconstant polyhedral differential inclusions. Both methods are sound for safety properties; that is, if we establish a safety property of the translated linear system, we may conclude that the original nonlinear system satisfies the property. When applicable, the clock translation is also complete for safety properties; that is, the original system and the translated system satisfy the same safety properties. The phaseportrait approximation method is not complete for safety properties, but it is asymptotically complete; intuitively, for every safety property, and for every relaxed nonlinear system arbitrarily close to the original, if the relaxed system satisfies the safety property, then there is a linear phaseportrait approximation that also satisfies the property. We illustrate both methods by using HYTECH—a symbolic model checker for linear hybrid automata—to automatically check properties of a nonlinear temperature controller and of a predator–prey ecology. Index Terms — Clock translation, formal verification, hybrid systems, HYTECH, linear hybrid automata, model checking, phaseportrait approximation, predator–prey ecologies.
Logics for Hybrid Systems
 Proceedings of the IEEE
, 2000
"... This paper offers a synthetic overview of, and original contributions to, the use of logics and formal methods in the analysis of hybrid systems ..."
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Cited by 137 (12 self)
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This paper offers a synthetic overview of, and original contributions to, the use of logics and formal methods in the analysis of hybrid systems
Symbolic Controller Synthesis for Discrete and Timed Systems
 Hybrid Systems II, LNCS 999
, 1995
"... . This paper presents algorithms for the symbolic synthesis of discrete and realtime controllers. At the semantic level the controller is synthesized by finding a winning strategy for certain games defined by automata or by timedautomata. The algorithms for finding such strategies need, this way o ..."
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Cited by 133 (16 self)
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. This paper presents algorithms for the symbolic synthesis of discrete and realtime controllers. At the semantic level the controller is synthesized by finding a winning strategy for certain games defined by automata or by timedautomata. The algorithms for finding such strategies need, this way or another, to search the statespace of the system which grows exponentially with the number of components. Symbolic methods allow such a search to be conducted without necessarily enumerating the statespace. This is achieved by representing sets of states using formulae (syntactic objects) over state variables. Although in the worst case such methods are as bad as enumerative ones, many huge practical problems can be treated by finetuned symbolic methods. In this paper the scope of these methods is extended from analysis to synthesis and from purely discrete systems to realtime systems. We believe that these results will pave the way for the application of program synthesis techniques to...
Reachability Analysis of Dynamical Systems having PiecewiseConstant Derivatives
 Theoretical Computer Science
, 1995
"... In this paper we consider a class of hybrid systems, namely dynamical systems with piecewiseconstant derivatives (PCD systems). Such systems consist of a partition of the Euclidean space into a finite set of polyhedral sets (regions). Within each region the dynamics is defined by a constant vector ..."
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Cited by 129 (20 self)
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In this paper we consider a class of hybrid systems, namely dynamical systems with piecewiseconstant derivatives (PCD systems). Such systems consist of a partition of the Euclidean space into a finite set of polyhedral sets (regions). Within each region the dynamics is defined by a constant vector field, hence discrete transitions occur only on the boundaries between regions where the trajectories change their direction. With respect to such systems we investigate the reachability question: Given an effective description of the systems and of two polyhedral subsets P and Q of the statespace, is there a trajectory starting at some x 2 P and reaching some point in Q? Our main results are a decision procedure for twodimensional systems, and an undecidability result for three or more dimensions. 1 Introduction 1.1 Motivation Hybrid systems (HS) are systems that combine intercommunicating discrete and continuous components. Most embedded systems belong to this class since they operate...