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114
Regular Model Checking
, 2000
"... . We present regular model checking, a framework for algorithmic verification of infinitestate systems with, e.g., queues, stacks, integers, or a parameterized linear topology. States are represented by strings over a finite alphabet and the transition relation by a regular lengthpreserving re ..."
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Cited by 165 (25 self)
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. We present regular model checking, a framework for algorithmic verification of infinitestate systems with, e.g., queues, stacks, integers, or a parameterized linear topology. States are represented by strings over a finite alphabet and the transition relation by a regular lengthpreserving relation on strings. Major problems in the verification of parameterized and infinitestate systems are to compute the set of states that are reachable from some set of initial states, and to compute the transitive closure of the transition relation. We present two complementary techniques for these problems. One is a direct automatatheoretic construction, and the other is based on widening. Both techniques are incomplete in general, but we give sufficient conditions under which they work. We also present a method for verifying !regular properties of parameterized systems, by computation of the transitive closure of a transition relation. 1 Introduction This paper presents regular ...
Model Checking in CLP
, 1999
"... We show that Constraint Logic Programming (CLP) can serve as a conceptual basis and as a practical implementation platform for the model checking of infinitestate systems. Our contributions are: (1) a semanticspreserving translation of concurrent systems into CLP programs, (2) a method for verifyi ..."
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Cited by 101 (28 self)
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We show that Constraint Logic Programming (CLP) can serve as a conceptual basis and as a practical implementation platform for the model checking of infinitestate systems. Our contributions are: (1) a semanticspreserving translation of concurrent systems into CLP programs, (2) a method for verifying safety and liveness properties on the CLP programs produced by the translation. We have implemented the method in a CLP system and verified wellknown examples of infinitestate programs over integers, using here linear constraints as opposed to Presburger arithmetic as in previous solutions.
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 70 (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.
Binary Reachability Analysis of Discrete Pushdown Timed Automata
 CAV'00, LNCS 1855
, 2000
"... . We introduce discrete pushdown timed automata that are timed automata with integervalued clocks augmented with a pushdown stack. A configuration of a discrete pushdown timed automaton includes a control state, finitely many clock values and a stack word. Using a pure automatatheoretic approa ..."
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Cited by 46 (28 self)
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. We introduce discrete pushdown timed automata that are timed automata with integervalued clocks augmented with a pushdown stack. A configuration of a discrete pushdown timed automaton includes a control state, finitely many clock values and a stack word. Using a pure automatatheoretic approach, we show that the binary reachability (i.e., the set of all pairs of configurations (ff; fi), encoded as strings, such that ff can reach fi through 0 or more transitions) can be accepted by a nondeterministic pushdown machine augmented with reversalbounded counters (NPCM). Since discrete timed automata with integervalued clocks can be treated as discrete pushdown timed automata without the pushdown stack, we can show that the binary reachability of a discrete timed automaton can be accepted by a nondeterministic reversalbounded multicounter machine. Thus, the binary reachability is Presburger. By using the known fact that the emptiness problem is decidable for reversalbounded ...
Combining widening and acceleration in linear relation analysis
 IN SAS
, 2006
"... Linear Relation Analysis [CH78,Hal79] is one of the first, but still one of the most powerful, abstract interpretations working in an infinite lattice. As such, it makes use of a widening operator to enforce the convergence of fixpoint computations. While the approximation due to widening can be ar ..."
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Cited by 45 (7 self)
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Linear Relation Analysis [CH78,Hal79] is one of the first, but still one of the most powerful, abstract interpretations working in an infinite lattice. As such, it makes use of a widening operator to enforce the convergence of fixpoint computations. While the approximation due to widening can be arbitrarily refined by delaying the application of widening, the analysis quickly becomes too expensive with the increase of delay. Previous attempts at improving the precision of widening are not completely satisfactory, since none of them is guaranteed to improve the precision of the result, and they can nevertheless increase the cost of the analysis. In this paper, we investigate an improvement of Linear Relation Analysis consisting in computing, when possible, the exact (abstract) effect of a loop. This technique is fully compatible with the use of widening, and whenever it applies, it improves both the precision and the performance of the analysis. Linear Relation Analysis [CH78,Hal79] (LRA) is one of the very first applications
Timed Automata and the Theory of Real Numbers
 CONCUR'99, LNCS 1664
, 1999
"... A configuration of a timed automaton is given by a control state and finitely many clock (real) values. We show here that the binary reachability relation between configurations of a timed automaton is definable in an additive theory of real numbers, which is decidable. This result implies the decid ..."
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Cited by 41 (0 self)
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A configuration of a timed automaton is given by a control state and finitely many clock (real) values. We show here that the binary reachability relation between configurations of a timed automaton is definable in an additive theory of real numbers, which is decidable. This result implies the decidability of model checking for some properties which cannot be expressed in timed temporal logics and provide with alternative proofs of some known decidable properties. Our proof is based on two intermediate results: 1. Every timed automaton can be effectively emulated by a timed automaton which does not contain nested loops. 2. The binary reachability relation for counter automata without nested loops (called here flat automata) is expressible in the additive theory of integers (resp. real numbers). The second result can be derived from [10]. 1 Introduction Timed automata have been introduced in [4] to model real time systems and became quickly a standard. They roughly consist in adding to...
Flat acceleration in symbolic model checking
 IN ATVA’05, VOLUME 3707 OF LNCS
, 2005
"... Symbolic model checking provides partially effective verification procedures that can handle systems with an infinite state space. Socalled “acceleration techniques” enhance the convergence of fixpoint computations by computing the transitive closure of some transitions. In this paper we develop a ..."
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Cited by 32 (15 self)
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Symbolic model checking provides partially effective verification procedures that can handle systems with an infinite state space. Socalled “acceleration techniques” enhance the convergence of fixpoint computations by computing the transitive closure of some transitions. In this paper we develop a new framework for symbolic model checking with accelerations. We also propose and analyze new symbolic algorithms using accelerations to compute reachability sets. Key words: verification of infinitestate systems, symbolic model checking, acceleration.
An AutomataTheoretic Approach to Constraint LTL
, 2003
"... We consider an extension of lineartime temporal logic (LTL) with constraints interpreted over a concrete domain. We use a new automatatheoretic technique to show pspace decidability of the logic for the constraint systems (Z, <, =) and (N, <, =). Along the way, we give an automatatheoretic ..."
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Cited by 32 (7 self)
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We consider an extension of lineartime temporal logic (LTL) with constraints interpreted over a concrete domain. We use a new automatatheoretic technique to show pspace decidability of the logic for the constraint systems (Z, <, =) and (N, <, =). Along the way, we give an automatatheoretic proof of a result of [BC02] when the constraint system D satisfies the completion property. Our decision procedures extend easily to handle extensions of the logic with past operators and constants, as well as an extension of the temporal language itself to monadic second order logic. Finally, we show that the logic...
Fast Acceleration of Ultimately Periodic Relations
, 2010
"... Abstract. Computing transitive closures of integer relations is the key to finding precise invariants of integer programs. In this paper, we describe an efficient algorithm for computing the transitive closures of difference bounds, octagonal and finite monoid affine relations. On the theoretical s ..."
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Cited by 30 (4 self)
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Abstract. Computing transitive closures of integer relations is the key to finding precise invariants of integer programs. In this paper, we describe an efficient algorithm for computing the transitive closures of difference bounds, octagonal and finite monoid affine relations. On the theoretical side, this framework provides a common solution to the acceleration problem, for all these three classes of relations. In practice, according to our experiments, the new method performs up to four orders of magnitude better than the previous ones, making it a promising approach for the verification of integer programs. 1
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.