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18
Revisiting Digitization, Robustness, and Decidability for Timed Automata
 In Proceedings of LICS 03
, 2003
"... We consider several questions related to the use of digitization techniques for timed automata. These very successful techniques reduce densetime language inclusion problems to discrete time, but are applicable only when the implementation is closed under digitization and the specification is close ..."
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Cited by 35 (6 self)
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We consider several questions related to the use of digitization techniques for timed automata. These very successful techniques reduce densetime language inclusion problems to discrete time, but are applicable only when the implementation is closed under digitization and the specification is closed under inverse digitization. We show that, for timed automata, the former (whether the implementation is closed under digitization) is decidable, but not the latter. We also investigate digitization questions in connection with the robust semantics for timed automata. The robust modelling approach introduces a timing fuzziness through the semantic removal of equality testing. Since its introduction half a decade ago, research into the robust semantics has suggested that it yields roughly the same theory as the standard semantics. This paper shows that, surprisingly, this is not the case: the robust semantics is significantly less tractable, and differs from the standard semantics in many key respects. In particular, the robust semantics yields an undecidable (nonregular) discretetime theory, in stark contrast with the standard semantics. This makes it virtually impossible to apply digitization techniques together with the robust semantics. On the positive side, we show that the robust languages of timed automata remain recursive.
Optimal semicomputable approximations to reachable and invariant sets
"... Optimal semicomputable approximations to reachable ..."
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Cited by 11 (4 self)
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Optimal semicomputable approximations to reachable
Safety Verification of Nonlinear Hybrid Systems is QuasiDecidable∗
, 2013
"... Safety verification of hybrid systems is undecidable, except for very special cases. In this paper, we circumvent undecidability by providing a verification algorithm that provably terminates for all robust problem instances, but need not necessarily terminate for nonrobust problem instances. A pro ..."
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Cited by 7 (1 self)
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Safety verification of hybrid systems is undecidable, except for very special cases. In this paper, we circumvent undecidability by providing a verification algorithm that provably terminates for all robust problem instances, but need not necessarily terminate for nonrobust problem instances. A problem instance x is robust iff the given property holds not only for x itself, but also when x is perturbed a little bit. Since, in practice, welldesigned hybrid systems are usually robust, this implies that the algorithm terminates for the cases occurring in practice. In contrast to earlier work, our result holds for a very general class of hybrid systems, and it uses a continuous time model. 1
Successive Abstractions of Hybrid Automata for Monotonic CTL Model Checking
"... Abstract. Current symbolic techniques for the automated reasoning over undecidable hybrid automata, force one to choose between the refinement of either an overapproximation or an underapproximation of the set of reachable states. When the analysis of branching time temporal properties is considere ..."
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Cited by 4 (2 self)
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Abstract. Current symbolic techniques for the automated reasoning over undecidable hybrid automata, force one to choose between the refinement of either an overapproximation or an underapproximation of the set of reachable states. When the analysis of branching time temporal properties is considered, the literature has developed a number of abstractions techniques based on the simulation preorder, that allow the preservation of only true universally quantified formulæ. This paper suggests a way to surmount these difficulties by defining a succession of abstractions of hybrid automata, which not only (1) allow the detection and the refinement of both over and underapproximated reachable sets symmetrically, but also (2) preserves the full set of branching time temporal properties (when interpreted on a dense time domain). Moreover, our approach imposes on the corresponding set of abstractions a desirable monotonicity property with respect to the set of modelchecked formulaæ. 1
Timed Automata for the Development of RealTime Systems
, 2011
"... Timed automata are a popular formalism to model realtime systems. They were introduced two decades ago to support formal verification. Since then they have also been used for other purposes and a large has been introduced to be able to deal with the many different kinds of requirements of realtime ..."
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Cited by 4 (0 self)
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Timed automata are a popular formalism to model realtime systems. They were introduced two decades ago to support formal verification. Since then they have also been used for other purposes and a large has been introduced to be able to deal with the many different kinds of requirements of realtime system. This paper presents a fairly comprehensive survey, comprised of eighty variants of timed automata. The paper classifies all these eighty variants of timed automata in an effort to determine current developments. It uses analysis techniques, formal properties, and decision problems to draw distinctions between different versions. Moreover, the paper discusses the challenges behind using a timed automata specification to derive an implementation of a working realtime system and presents some solutions. Finally, the paper lists and classifies forty tools supporting timed automata. The paper does not only discuss many variants and their supporting concepts (e.g., closure properties, decision problems), techniques (e.g., for analysis), and tools, but it also attempts to help the reader navigate the vast literature in the field, to highlight differences and similarities between variants, and to reveal research trends and promising avenues for future exploration.
Algebraic Systems Biology: Theses and Hypotheses
 Proceedings of Algebraic Biology 2007 – Second International Conference, 4545:1–14
, 2007
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A Uniform Approach to ThreeValued Semantics for µCalculus on Abstractions of Hybrid Automata
"... Abstract. Abstraction/refinement methods play a central role in the analysis of hybrid automata, that are rarely decidable. Soundness (of evaluated properties) is a major challenge for these methods, since abstractions can introduce unrealistic behaviors. In this paper, we consider the definition of ..."
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Abstract. Abstraction/refinement methods play a central role in the analysis of hybrid automata, that are rarely decidable. Soundness (of evaluated properties) is a major challenge for these methods, since abstractions can introduce unrealistic behaviors. In this paper, we consider the definition of a threevalued semantics for μcalculus on abstractions of hybrid automata. Our approach relies on two steps: First, we develop a framework that is general in the sense that it provides a preservation result that holds for several possible semantics of the modal operators. In a second step, we instantiate our framework to two particular abstractions. To this end, a key issue is the consideration of both over and underapproximated reachability analysis, while classic simulationbased abstractions rely only on overapproximations, and limit the preservation to the universal (μcalculus’) fragment. To specialize our general result, we consider (1) socalled discrete bounded bisimulation abstractions, and (2) modal abstractions based on may/must transitions. 1
Mortality of Iterated Piecewise Affine Functions over the Integers: Decidability and Complexity
, 2013
"... In the theory of discretetime dynamical systems one studies the limiting behaviour of processes defined by iterating a fixed function f over a given space. A muchstudied case involves piecewise affine functions on Rn. Blondel et al. (2001) studied the decidability of questions such as global conve ..."
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In the theory of discretetime dynamical systems one studies the limiting behaviour of processes defined by iterating a fixed function f over a given space. A muchstudied case involves piecewise affine functions on Rn. Blondel et al. (2001) studied the decidability of questions such as global convergence and mortality for such functions with rational coefficients. Mortality means that every trajectory includes a 0; if the iteration is implemented as a loop while (x = 0) x: = f(x), mortality means that the loop is guaranteed to terminate. Checking the termination of simple loops (under various restrictions of the guard and the update function) is a muchstudied topic in automated program analysis. Blondel et al. proved that the problems are undecidable when the state space is R n (or Q n), and the dimension n is at least two. From a program analysis (and discrete Computability) viewpoint, it is more natural to consider functions over the integers. This paper establishes (un)decidability results for the integer setting. We show that also over integers, undecidability (moreover, Π 0 2 completeness) begins at two dimensions. We further investigate the effect of several restrictions on the iterated functions. Specifically, we consider bounding the size of the partition defining f, and restricting the coefficients of the linear components. In the decidable cases, we give complexity results. The complexity is PTIME for affine functions, but for piecewiseaffine ones it is PSPACEcomplete. The undecidability proofs use some variants of the Collatz problem, which may be of independent interest. 1
Transferring Causality Analysis from Synchronous Programs to Hybrid Programs
"... Outputs of synchronous programs may suffer from cyclic dependencies since statements are allowed to read the current outputs ’ values to determine the actions that generate the current values of the outputs. For this reason, compilers have to perform a causality analysis that ensures that at any poi ..."
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Outputs of synchronous programs may suffer from cyclic dependencies since statements are allowed to read the current outputs ’ values to determine the actions that generate the current values of the outputs. For this reason, compilers have to perform a causality analysis that ensures that at any point of time, there is a unique and constructive way to determine the outputs. The discrete parts of hybrid systems may suffer from the same problem as observed in synchronous programs. As we recently extended our synchronous language Quartz to describe hybrid systems, we explain in this paper how the causality analysis as originally introduced for synchronous systems can also be used to handle cyclic dependencies in hybrid Modelica programs. 1
B.: Algorithmic algebraic model checking II
 In Peled, D., Tsay, Y.K., eds.: ATVA. Volume 3707 of LNCS
, 2005
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