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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.
HyTech: A Model Checker for Hybrid Systems
 Software Tools for Technology Transfer
, 1997
"... A hybrid system is a dynamical system whose behavior exhibits both discrete and continuous change. A hybrid automaton is a mathematical model for hybrid systems, which combines, in a single formalism, automaton transitions for capturing discrete change with differential equations for capturing conti ..."
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Cited by 356 (6 self)
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A hybrid system is a dynamical system whose behavior exhibits both discrete and continuous change. A hybrid automaton is a mathematical model for hybrid systems, which combines, in a single formalism, automaton transitions for capturing discrete change with differential equations for capturing continuous change. HyTech is a symbolic model checker for linear hybrid automata, a subclass of hybrid automata that can be analyzed automatically by computing with polyhedral state sets. A key feature of HyTech is its ability to perform parametric analysis, i.e. to determine the values of design parameters for which a linear hybrid automaton satisfies a temporallogic requirement. 1 Introduction A hybrid system typically consists of a collection of digital programs that interact with each other and with an analog environment. Examples of hybrid systems include manufacturing controllers, automotive and flight controllers, medical equipment, microelectromechanical systems, and robots. When thes...
HYTECH: The next generation
 In Proceedings of the 16th IEEE RealTime Systems Symposium
, 1995
"... Abstract. We describe a new implementation of HyTech 1,asymbolic model checker for hybrid systems. Given a parametric description of an embedded system as a collection of communicating automata, HyTech automatically computes the conditions on the parameters under which the system satis es its safety ..."
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Cited by 102 (7 self)
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Abstract. We describe a new implementation of HyTech 1,asymbolic model checker for hybrid systems. Given a parametric description of an embedded system as a collection of communicating automata, HyTech automatically computes the conditions on the parameters under which the system satis es its safety and timing requirements. While the original HyTech prototype was based on the symbolic algebra tool Mathematica, the new implementation is written in C ++ and builds on geometric algorithms instead of formula manipulation. The new HyTech o ers a cleaner and more expressive input language, greater portability, superior performance (typically two to three orders of magnitude), and new features such as diagnostic errortrace generation. We illustrate the e ectiveness of the new implementation by applying HyTech to the automatic parametric analysis of the generic railroad crossing benchmark problem [HJL93] and to an active structure control algorithm [ECB94]. 1
Verification of an Audio Protocol with Bus Collision Using UPPAAL
, 1996
"... In this paper we apply the tool Uppaal to an automatic analysis of a version of the Philips Audio Control Protocol with two senders and bus collision handling. This case study is significantly larger than the realtime/hybrid systems previously analysed by automatic tools. During the case study the ..."
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Cited by 57 (24 self)
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In this paper we apply the tool Uppaal to an automatic analysis of a version of the Philips Audio Control Protocol with two senders and bus collision handling. This case study is significantly larger than the realtime/hybrid systems previously analysed by automatic tools. During the case study the tool Uppaal was extended with a new feature, committed locations, allowing efficient modelling of broadcast communication.
Hybrid Automata with Finite Bisimulations
, 1995
"... . The analysis, verification, and control of hybrid automata with finite bisimulations can be reduced to finitestate problems. We advocate a timeabstract, phasebased methodology for checking if a given hybrid automaton has a finite bisimulation. First, we factor the automaton into two components, ..."
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Cited by 57 (6 self)
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. The analysis, verification, and control of hybrid automata with finite bisimulations can be reduced to finitestate problems. We advocate a timeabstract, phasebased methodology for checking if a given hybrid automaton has a finite bisimulation. First, we factor the automaton into two components, a boolean automaton with a discrete dynamics on the finite state space B m and a euclidean automaton with a continuous dynamics on the infinite state space R n . Second, we investigate the phase portrait of the euclidean component. In this fashion, we obtain new decidability results for hybrid systems as well as new, uniform proofs of known decidability results. For example, we prove that if two hybrid automata have finite bisimulations, and both can be calibrated to a common time scale, then their product also has a finite bisimulation. 1 Introduction A hybrid automaton [2] is a mathematical model for a digital program that interacts with an analog environment. Hybrid automata are usef...
Reachability Verification for Hybrid Automata
 HSCC 98: HYBRID SYSTEMS—COMPUTATION AND CONTROL, LECTURE NOTES IN COMPUTER SCIENCE 1386
, 1998
"... We study the reachability problem for hybrid automata. Automatic approaches, which attempt to construct the reachable region by symbolic execution, often do not terminate. In these cases, we require the user to guess the reachable region, and we use a theorem prover (Pvs) to verify the guess. We cl ..."
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Cited by 9 (0 self)
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We study the reachability problem for hybrid automata. Automatic approaches, which attempt to construct the reachable region by symbolic execution, often do not terminate. In these cases, we require the user to guess the reachable region, and we use a theorem prover (Pvs) to verify the guess. We classify hybrid automata according to the theory in which their reachable region can be defined finitely. This is the theory in which the prover needs to operate in order to verify the guess. The approach is interesting, because an appropriate guess can often be deduced by extrapolating from the first few steps of symbolic execution.
Constrained Regular Approximation of Logic Programs
 In Logic Programming Synthesis and Transformation (Selected Papers
, 1997
"... Abstract. Regular approximation is a wellknown and useful analysis technique for conventional logic programming. Given the existence of constraint solving techniques, one may wish to obtain more precise approximations of programs while retaining the decidable properties of the approximation. Greate ..."
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Cited by 5 (3 self)
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Abstract. Regular approximation is a wellknown and useful analysis technique for conventional logic programming. Given the existence of constraint solving techniques, one may wish to obtain more precise approximations of programs while retaining the decidable properties of the approximation. Greater precision could increase the e ectiveness of applications that make use of regular approximation, such as the detection of useless clauses and type analysis. In this paper, we introduce arithmetic constraints, based on convex polyhedra, into regular approximation. In addition, Herbrand constraints can be introduced to capture dependencies among arguments.
A Framework to Analyse Synchronous DataFlow Specifications
, 1402
"... Presence and absence of signals inside a reaction are inherent to the synchronous paradigm, as well as clocks which are sets of instants that indicate when a given condition is fulfilled over a sequence of reactions (e.g. when a signal is present). Clocks are essential to capture the control in data ..."
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Presence and absence of signals inside a reaction are inherent to the synchronous paradigm, as well as clocks which are sets of instants that indicate when a given condition is fulfilled over a sequence of reactions (e.g. when a signal is present). Clocks are essential to capture the control in dataflow specifications; more generally relations between clocks should be analyzed to verify some properties, e.g. to detect inconsistencies in specifications. These relations express particular safety properties many of which can be verified without considering the dynamic of systems, by means of a static abstraction. We propose a language CL to describe such properties and prove it decidable. Modelchecking is derived for Signal programs, on the basis of a translation from the static abstraction of Signal into CL.