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Modeling and Verifying Systems using a Logic of Counter Arithmetic with Lambda Expressions and Uninterpreted Functions
, 2002
"... In this paper, we present the logic of Counter arithmetic with Lambda expressions and Uninterpreted functions (CLU). CLU generalizes the logic of equality with uninterpreted functions (EUF) with constrained lambda expressions, ordering, and successor and predecessor functions. In addition to mod ..."
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Cited by 156 (43 self)
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In this paper, we present the logic of Counter arithmetic with Lambda expressions and Uninterpreted functions (CLU). CLU generalizes the logic of equality with uninterpreted functions (EUF) with constrained lambda expressions, ordering, and successor and predecessor functions. In addition to modeling pipelined processors that EUF has proved useful for, CLU can be used to model many infinitestate systems including those with infinite memories, finite and infinite queues including lossy channels, and networks of identical processes. Even with this richer expressive power, the validity of a CLU formula can be efficiently decided by translating it to a propositional formula, and then using Boolean methods to check validity. We give theoretical and empirical evidence for the efficiency of our decision procedure. We also describe verification techniques that we have used on a variety of systems, including an outoforder execution unit and the loadstore unit of an industrial microprocessor.
How to compose PresburgerAccelerations: Applications to Broadcast Protocols
 IN PROC. 22ND CONF. FOUND. OF SOFTWARE TECHNOLOGY AND THEOR. COMP. SCI. (FST&TCS'2002), KANPUR
, 2002
"... Finite linear systems are finite sets of linear functions whose guards are de fined by Presburger formulas, and whose the squares matrice associated generate a finite multiplicative monoid. We prove that for finite linear systems, the accelerations of sequences of transitions always produce an effec ..."
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Cited by 73 (19 self)
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Finite linear systems are finite sets of linear functions whose guards are de fined by Presburger formulas, and whose the squares matrice associated generate a finite multiplicative monoid. We prove that for finite linear systems, the accelerations of sequences of transitions always produce an effective Presburgerdefinable relation. We then show how to choose the good sequences of length n whose number is polynomial in n although the total number of cycles of length n is exponential in n. We implement these theoretical results in the tool FAST [FAS] (Fast Acceleration of Symbolic Transition systems). FAST computes in few seconds the minimal deterministic finite automata that represent the reachability sets of 8 wellknown broadcast protocols.
Iterating Transducers
, 2001
"... Regular languages have proved useful for the symbolic state exploration of infinite state systems. They can be used to represent infinite sets of system configurations; the transitional semantics of the system consequently can be modeled by finitestate transducers. A standard problem encountered ..."
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Cited by 32 (0 self)
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Regular languages have proved useful for the symbolic state exploration of infinite state systems. They can be used to represent infinite sets of system configurations; the transitional semantics of the system consequently can be modeled by finitestate transducers. A standard problem encountered when doing symbolic state exploration for infinite state systems is how to explore all states in a finite amount of time. When representing the onestep transition relation of a system by a finitestate transducer T , this problem boils down to finding an appropriate finitestate representation T for its transitive closure. In this
Flatness is not a Weakness
, 2000
"... We propose an extension, called L + p , of the temporal logic LTL, which enables talking about finitely many register values: the models are infinite words over tuples of integers (resp. real numbers). The formulas of L + p are flat: on the left of an until, only atomic formulas or LTL formu ..."
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Cited by 31 (0 self)
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We propose an extension, called L + p , of the temporal logic LTL, which enables talking about finitely many register values: the models are infinite words over tuples of integers (resp. real numbers). The formulas of L + p are flat: on the left of an until, only atomic formulas or LTL formulas are allowed. We prove, in the spirit of the correspondence between automata and temporal logics, that the models of a L + p formula are recognized by a piecewise flat counter machine; for each state q, at most one loop of the machine on q may modify the register values. Emptiness of (piecewise) flat counter machines is decidable (this follows from a result in [9]). It follows that satisfiability and modelchecking the negation of a formula are decidable for L + p . On the other hand, we show that inclusion is undecidable for such languages. This shows that validity and modelchecking positive formulas are undecidable.
Regular Model Checking made Simple and Efficient
"... We present a new technique for computing the transitive closure of a regular relation characterized by a finitestate transducer. The construction starts from the original transducer, and repeatedly adds new transitions which are compositions of currently existing transitions. ..."
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Cited by 30 (15 self)
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We present a new technique for computing the transitive closure of a regular relation characterized by a finitestate transducer. The construction starts from the original transducer, and repeatedly adds new transitions which are compositions of currently existing transitions.
Parameterized Reachability Analysis of the IEEE 1394 Root Contention Protocol using TReX
 PROCEEDINGS OF THE WORKSHOP ON REALTIME TOOLS (RTTOOLS'2001)
, 2001
"... We report about the reachability analysis of fully parametrized models of the IEEE 1394 root contention protocol. This protocol uses timing constraints in order to elect a leader. The interesting point is that the timing constraints involve some parameters (transmission delay, bounds of waiting i ..."
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Cited by 14 (0 self)
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We report about the reachability analysis of fully parametrized models of the IEEE 1394 root contention protocol. This protocol uses timing constraints in order to elect a leader. The interesting point is that the timing constraints involve some parameters (transmission delay, bounds of waiting intervals), and the behavior of the protocol strongly depends on the relation between these parameters. In order to synthesize the relation ensuring the correct behavior of the protocol, we apply the symbolic reachability techniques implemented in the TReX tool. We take the unparameterized model of Root Contention protocol proposed in [24] and study different parametrized versions of this model. We are able to synthesize automatically all the relations already found by proof or experiments on the unparameterized versions. We compare our results with those reported or obtained using other tools for parametrized systems.
Bisimulation and other undecidable equivalences for lossy channel systems
 In Proc. of TACS’01, volume 2215 of LNCS
, 2001
"... Abstract. Lossy channel systems are systems of finite state automata that communicate via unreliable unbounded fifo channels. Today the main open question in the theory of lossy channel systems is whether bisimulation is decidable. We show that bisimulation, simulation, and in fact all relations bet ..."
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Cited by 8 (0 self)
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Abstract. Lossy channel systems are systems of finite state automata that communicate via unreliable unbounded fifo channels. Today the main open question in the theory of lossy channel systems is whether bisimulation is decidable. We show that bisimulation, simulation, and in fact all relations between bisimulation and trace inclusion are undecidable for lossy channel systems (and for lossy vector addition systems). 1
A Transformational Approach for Generating NonLinear Invariants
 IN STATIC ANALYSIS SYMPOSIUM (JUNE 2000
, 2000
"... Computing invariants is the key issue in the analysis of infinitestate systems whether analysis means testing, verification or parameter synthesis. In particular, methods that allow to treat combinations of loops are of interest. We present a set of algorithms and methods that can be applied to cha ..."
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Cited by 7 (0 self)
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Computing invariants is the key issue in the analysis of infinitestate systems whether analysis means testing, verification or parameter synthesis. In particular, methods that allow to treat combinations of loops are of interest. We present a set of algorithms and methods that can be applied to characterize overapproximations of the set of reachable states of combinations of selfloops. We present two families of complementary techniques. The first one identifies a number of basic cases of pair of selfloops for which we provide an exact characterization of the reachable states. The second family of techniques is a set of rules based on static analysis that allow to reduce n selfloops (n 2) to n  1 independent pairs of selfloops. The results of the analysis of the pairs of selfloops can then be combined to provide an overapproximation of the reachable states of the n selfloops. We illustrate our methods by synthesizing conditions under which the Biphase Mark protocol works proper...
Contrôle de systemes symboliques, discrets ou hybrides
, 2005
"... ... abordons le probleme de la synthese de contr^oleurs a travers differents modeles allant des systemes de transitions nis aux systemes hybrides en nous interessant a des proprietes de s^urete. Dans ce cadre, nous nous interessons principalement au probleme de synthese pour un modele intermediaire: ..."
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Cited by 3 (0 self)
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... abordons le probleme de la synthese de contr^oleurs a travers differents modeles allant des systemes de transitions nis aux systemes hybrides en nous interessant a des proprietes de s^urete. Dans ce cadre, nous nous interessons principalement au probleme de synthese pour un modele intermediaire: les systemes de transitions symboliques. L'analyse des besoins de modelisation nous amene a rede nir la notion de contr^olabilite en faisant porter le caractere de contr^olabilite non plus sur les evenements mais sur les gardes des transitions, puis a de nir des algorithmes de synthese permettant l'usage d'approximations d'assurer la nitude des calculs. Nous generalisons par la suite notre methodologie au contr^ole de systemes hybrides, ce qui donne un cadre uni e du probleme de la synthese pour un ensemble consistant de modeles.
Iterating Transducers for Safety of DataAbstractions
, 2000
"... Regular languages have proved useful for the symbolic state exploration of infinite state systems. Regular languages can be used to represent infinite sets of system configurations, the transitional semantics of the system consequently can be modeled by finitestate transducers. A standard problem e ..."
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Cited by 1 (0 self)
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Regular languages have proved useful for the symbolic state exploration of infinite state systems. Regular languages can be used to represent infinite sets of system configurations, the transitional semantics of the system consequently can be modeled by finitestate transducers. A standard problem encountered when doing symbolic state exploration for in nite state systems is, how to explore all states in a finite amount of time. When representing the onestep transition relation of a system by a finitestate transducer T , this problem boils down to finding a finitestate representation for T , capturing the transitive closure of the onestep reduction relation. In this paper we give a semialgorithm to compute T . The construction is based on building a quotient of an infinitestate representation, where the quotienting uses past and future bisimulations computed on finite approximations of T . As in general, T is not representable by a finitestate transducer, the constructi...