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On Decidability of Prebisimulation for Timed Automata
"... Abstract. In this paper, we propose an at least as fast as relation between two timed automata states and investigate its decidability. The proposed relation is a prebisimulation and we show that given two processes with rational clock valuations it is decidable whether such a prebisimulation relati ..."
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Abstract. In this paper, we propose an at least as fast as relation between two timed automata states and investigate its decidability. The proposed relation is a prebisimulation and we show that given two processes with rational clock valuations it is decidable whether such a prebisimulation relation exists between them. Though bisimulation relations have been widely studied with respect to timed systems and timed automata, prebisimulations in timed systems form a much lesser studied area and according to our knowledge, this is the first of the kind where we study the decidability of a timed prebisimulation. This prebisimulation has been termed timed performance prebisimulation since it compares the efficiency of two states in terms of their performances in performing actions. s � t if s and t are time abstracted bisimilar and every possible delay by s and its successors is no more than the delays performed by t and its successors where the delays are real numbers. The prebisimilarity defined here falls in between timed and time abstracted bisimilarity. Key words: Timed automata, timed bisimulation, time abstracted bisimulation, prebisimulation, timed transition system 1
Model checking of systems employing commutative functions
- 6th International Conference on Verification, Model Checking and Abstract Interpretation, Lecture Notes in Computer Science
, 2005
"... Abstract. The paper presents methods for model checking a class of possibly infinite state concurrent programs using various types of bi-simulation reductions. The proposed methods work for the class of programs in which the functions that update the variables are mutually commutative. A number of b ..."
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Abstract. The paper presents methods for model checking a class of possibly infinite state concurrent programs using various types of bi-simulation reductions. The proposed methods work for the class of programs in which the functions that update the variables are mutually commutative. A number of bi-simulation relations are presented for such systems. Explicit state model checking methods that employ on-the-fly reductions with respect to these bisimulations are given. Some of these methods have been implemented and have been used to verify some well known protocols that employ integer variables. Various applications of the methods and optimization techniques for special cases are also given in appendix. 1 Introduction Two of the bottlenecks that hinder wider applicability of model checking approach is the state explosion problem and its less effectiveness in handling infinite state systems. In this paper, we present an approach for model checking that works for certain classes of infinite state systems and that can also be used to contain the state explosion problem. One standard model checking method, employed often, is to construct the reachability graph of the given program and then check the correctness property against this graph. One way of reducing the size of the explored graph is to employ a reduction with respect to a bi-simulation relation U on the states of the reachability graph. Such a relation U is either known a priori through an implicit representation or has been computed by other means.
Optimizing timed automata model checking via clock reordering
- IN: 27 TH IEEE INTERNATIONAL REAL-TIME SYSTEMS SYMPOSIUM, WORK IN PROGRESS SESSION, IEEE (2006
"... An essential operation in timed automata model checking is inclusion checking which decides whether a set of states, represented as a convex polyhedron, is included in another set. Several verification tools implement convex polyhedra as square matrixes called DBMs (short for Difference Bound Matrix ..."
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An essential operation in timed automata model checking is inclusion checking which decides whether a set of states, represented as a convex polyhedron, is included in another set. Several verification tools implement convex polyhedra as square matrixes called DBMs (short for Difference Bound Matrix), where each row and column is associated to a clock in the system under analysis. An element in the matrix represents the bound for the value of a clock or for the difference between two clocks. Inclusion checking can be called hundreds of millions of times during the verification of a medium-size model. The naïve implementation scans each matrix cell by cell and compares it against the corresponding one in the other matrix. If all the checks are successful the first matrix is included into the second. If one of them fails, it is not. In the last case, the order in which matrixes are traversed is decisive for the inclusion checking's efficiency. In this article we present a clock reordering technique which reduces the number of comparisons needed to find a failure. Experiments show neglectable memory overhead and time savings of up to 17%.
A Unifying Approach to Decide Relations for Timed Automata and their Game Characterization
"... In this paper we present a unifying approach for deciding various bisimulations, simulation equiv-alences and preorders between two timed automata states. We propose a zone based method for deciding these relations in which we eliminate an explicit product construction of the region graphs or the zo ..."
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In this paper we present a unifying approach for deciding various bisimulations, simulation equiv-alences and preorders between two timed automata states. We propose a zone based method for deciding these relations in which we eliminate an explicit product construction of the region graphs or the zone graphs as in the classical methods. Our method is also generic and can be used to de-cide several timed relations. We also present a game characterization for these timed relations and show that the game hierarchy reflects the hierarchy of the timed relations. One can obtain an infinite game hierarchy and thus the game characterization further indicates the possibility of defining new timed relations which have not been studied yet. The game characterization also helps us to come up with a formula which encodes the separation between two states that are not timed bisimilar. Such distinguishing formulae can also be generated for many relations other than timed bisimilarity. 1
Anonymized Reachability of Hybrid Automata Networks
"... Abstract. In this paper, we present a method for computing the set of reachable states for networks consisting of the parallel composition of a finite number of the same hybrid automaton template with rectangular dynamics. The method utilizes a symmetric representation of the set of reachable state ..."
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Abstract. In this paper, we present a method for computing the set of reachable states for networks consisting of the parallel composition of a finite number of the same hybrid automaton template with rectangular dynamics. The method utilizes a symmetric representation of the set of reachable states (modulo the automata indices) that we call anonymized states, which makes it scalable. Rather than explicitly enumerating each automaton index in formulas representing sets of states, the anonymized representation encodes only: (a) the classes of automata, which are the states of automata represented with formulas over symbolic indices, and (b) the number of automata in each of the classes. We present an algorithm for overapproximating the reachable states by computing state transitions in this anonymized representation. Unlike symmetry reduction techniques used in finite state models, the timed transition of a network composed of hybrid automata causes the continuous variables of all the automata to evolve simultaneously. The anonymized representation is amenable to both reducing the discrete and continuous complexity. We evaluate a prototype implementation of the representation and reachability algorithm in our satisfiability modulo theories (SMT)-based tool, Passel. Our experimental results are promising, and generally allow for scaling to networks composed of tens of automata, and in some instances, hundreds (or more) of automata.
Agata Janowska Pawe̷l Janowski Slicing of Timed Automata with Discrete Data*
, 2006
"... The paper proposes how to use static analysis to extract an abstract model of a system. The method uses techniques of program slicing to examine syntax of a system modeled as a set of timed automata with discrete data, a common input formalism of model checkers dealing with time. The method is prope ..."
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The paper proposes how to use static analysis to extract an abstract model of a system. The method uses techniques of program slicing to examine syntax of a system modeled as a set of timed automata with discrete data, a common input formalism of model checkers dealing with time. The method is property driven. The abstraction is exact with respect to all properties expressed in the temporal logic CTL X*.
Controller Syntehsis and Scheduling Algorithms G. Behrmann: ”Guiding and Cost Optimizing UPPAAL”.
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Web Portal for Benchmarking Explicit Model Checkers
, 2006
"... Reproduction of all or part of this work is permitted for educational or research use on condition that this copyright notice is included in any copy. Publications in the FI MU Report Series are in general accessible via WWW: ..."
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Reproduction of all or part of this work is permitted for educational or research use on condition that this copyright notice is included in any copy. Publications in the FI MU Report Series are in general accessible via WWW:
Decomposition of Decidable First-Order Logics over Integers and Reals
"... We tackle the issue of representing infinite sets of real-valued vectors. This paper introduces an operator for combining integer and real sets. Using this operator, we decompose three well-known logics extending Presburger with reals. Our decomposition splits a logic into two parts: one integer, an ..."
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We tackle the issue of representing infinite sets of real-valued vectors. This paper introduces an operator for combining integer and real sets. Using this operator, we decompose three well-known logics extending Presburger with reals. Our decomposition splits a logic into two parts: one integer, and one decimal (i.e. on the interval [0, 1[). We also give a basis for an implementation of our representation.
