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131
On the Synthesis of Discrete Controllers for Timed Systems
 in E.W. Mayr and C. Puech (Eds), Proc. STACS'95, LNCS 900
, 1995
"... Abstract. This paper presents algorithms for the automatic synthesis of realtime controllers by nding a winning strategy for certain games de ned by the timedautomata of Alur and Dill. In such games, the outcome depends on the players ' actions as well as on their timing. We believe that these res ..."
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Cited by 190 (20 self)
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Abstract. This paper presents algorithms for the automatic synthesis of realtime controllers by nding a winning strategy for certain games de ned by the timedautomata of Alur and Dill. In such games, the outcome depends on the players ' actions as well as on their timing. We believe that these results will pave theway for the application of program synthesis techniques to the construction of realtime embedded systems from their speci cations. 1
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 123 (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.
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 112 (29 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...
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 111 (18 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...
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 108 (17 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...
Effective Synthesis of Switching Controllers for Linear Systems
, 2000
"... In this work we suggest a novel methodology for synthesizing switching controllers for continuous and hybrid systems whose dynamics are defined by linear differential equations. We formulate the synthesis problem as finding the conditions upon which a controller should switch the behavior of the sys ..."
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Cited by 78 (8 self)
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In this work we suggest a novel methodology for synthesizing switching controllers for continuous and hybrid systems whose dynamics are defined by linear differential equations. We formulate the synthesis problem as finding the conditions upon which a controller should switch the behavior of the system from one "mode" to another in order to avoid a set of bad states, and propose an abstract algorithm which solves the problem by an iterative computation of reachable states. We have implemented a concrete version of the algorithm, which uses a new approximation scheme for reachability analysis of linear systems.
Timing Analysis of Asynchronous Circuits using Timed Automata
 in P.E. Camurati, H. Eveking (Eds.), Proc. CHARME'95, LNCS 987
, 1995
"... Abstract. In this paper we present a method for modeling asynchronous digital circuits by timed automata. The constructed timed automata serve as\mechanical " and veri able objects for asynchronous sequential machines in the same sense that (untimed) automata do for synchronous machines. These ..."
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Cited by 59 (14 self)
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Abstract. In this paper we present a method for modeling asynchronous digital circuits by timed automata. The constructed timed automata serve as\mechanical " and veri able objects for asynchronous sequential machines in the same sense that (untimed) automata do for synchronous machines. These results, combined with recent results concerning the analysis and synthesis of timed automata provide for the systematic treatment of a large class of problems that could be treated by conventional simulation methods only in an adhoc fashion. The problems that can be solved due to the results presented in this paper include: the reachability analysis of a circuit with uncertainties in gate delays and input arrival times, inferring the necessary timing constraints on input signals that guaranteeaproper functioning of a circuit and calculating the delay characteristics of the components required inorder to meet some given behavioral speci cations. Notwithstanding the existence of negative theoretical results concerning the worstcase complexity of timed automata analysis algorithms, initial experimentation with the Kronos tool for timing analysis suggest that timed automata derived from circuits might not be so hard to analyze in practice. 1
A Kleene Theorem for Timed Automata
, 1997
"... In this paper we define timed regular expressions, an extension of regular expressions for specifying sets of densetime discretevalued signals. We show that this formalism is equivalent in expressive power to the timed automata of Alur and Dill by providing a translation procedure from expressions ..."
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Cited by 55 (2 self)
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In this paper we define timed regular expressions, an extension of regular expressions for specifying sets of densetime discretevalued signals. We show that this formalism is equivalent in expressive power to the timed automata of Alur and Dill by providing a translation procedure from expressions to automata and vice versa. The result is extended to !regular expressions (B uchi's theorem). 1. Introduction Timed automata, i.e. automata equipped with clocks [AD94], have been studied extensively in recent years as they provide a rigorous model for reasoning about the quantitative temporal aspects of systems. Together with realtime logics and process algebras they constitute the underlying theoretical basis for the specification and verification of realtime systems. Kleene's theorem [K56], stating that the regular (or rational) subsets of \Sigma are exactly the recognizable ones (those accepted by finite automata), is one of the cornerstones of automata theory. No such theorem has ...
Symbolic Model Checking of Probabilistic Timed Automata Using Backwards Reachability
, 2000
"... We consider probabilistic timed automata of [13], an extension of the timed automata model of [2] with discrete probability distributions. In contrast to timed automata, which model realtime systems purely in terms of nondeterminism, our model allows to express the likelihood of the system makin ..."
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Cited by 49 (18 self)
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We consider probabilistic timed automata of [13], an extension of the timed automata model of [2] with discrete probability distributions. In contrast to timed automata, which model realtime systems purely in terms of nondeterminism, our model allows to express the likelihood of the system making certain transitions, and is thus appropriate for modelling faulttolerance and probabilistic failures. We present a symbolic model checking algorithm for the existential fragment of the logic PTCTL of [13] based on backward reachability as in [12]. The logic allows us to specify properties such as \with probability 0.99 or greater, it is possible to correctly deliver a data packet within 5 time units", or \with probability 0.87 or greater, the system never enters an error state".
Some progress in the symbolic verification of timed automata
 IN PROC. OF THE 8TH CONFERENCE ON COMPUTERAIDED VERI CATION
, 1997
"... In this paper we discuss the practical difficulty of analyzing the behavior of timed automata and report some results obtained using an experimental bddbased extension of kronos. We have treated examples originating from timing analysis of asynchronous boolean networks and CMOS circuits with delay ..."
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Cited by 49 (4 self)
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In this paper we discuss the practical difficulty of analyzing the behavior of timed automata and report some results obtained using an experimental bddbased extension of kronos. We have treated examples originating from timing analysis of asynchronous boolean networks and CMOS circuits with delay uncertainties and the results outperform those obtained by previous implementations of timed automata verification tools.