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A Methodological View of Constraint Solving
, 1996
"... Constraints have become very popular during the last decade. Constraints allow to define sets of data by means of logical formulae. Our goal here is to survey the notion of constraint system and to give examples of constraint systems operating on various domains, such as natural, rational or real nu ..."
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Cited by 6 (2 self)
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the paper to illustrate the concepts and methods. We also discuss applications of constraints to various fields, such as programming, operations research, and theorem proving. y CNRS and LRI, Bat. 490, Universit'e de Paris Sud, 91405 ORSAY Cedex, France fcomon, jouannaudg@lri.lri.fr z COSYTEC, Parc
Multiple counters automata, safety analysis and Presburger arithmetic
, 1998
"... We consider automata with counters whose values are updated according to signals sent by the environment. A transition can be fired only if the values of the counters satisfy some guards (the guards of the transition). We consider guards of the form y i #y j +c i;j where y i is either x 0 i or ..."
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Cited by 117 (1 self)
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We consider automata with counters whose values are updated according to signals sent by the environment. A transition can be fired only if the values of the counters satisfy some guards (the guards of the transition). We consider guards of the form y i #y j +c i;j where y i is either x 0 i or x i , the values of the counter i respectively after and before the transition, and # is any relational symbol in f=; ; ; ?; !g. We show that the set of possible counter values which can be reached after any number of iterations of a loop is definable in the additive theory of N (or Z or R depending on the type of the counters). This result can be used for the safety analysis of multiple counters automata.
New Decidability Results for Fragments of FirstOrder Logic and Application to Cryptographic Protocols
, 2003
"... We consider a new extension of the Skolem class for firstorder logic and prove its decidability by resolution techniques. We then extend this class including the builtin equational theory of exclusive or. Again, we prove the decidability of the class by resolution techniques. ..."
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Cited by 54 (18 self)
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We consider a new extension of the Skolem class for firstorder logic and prove its decidability by resolution techniques. We then extend this class including the builtin equational theory of exclusive or. Again, we prove the decidability of the class by resolution techniques.
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...
Equational Formulae with Membership Constraints
 Information and Computation
, 1994
"... We propose a set of transformation rules for first order formulae whose atoms are either equations between terms or "membership constraints" t 2 i. i can be interpreted as a regular tree language (i is called a sort in the algebraic specification community) or as a tree language in any cla ..."
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Cited by 38 (3 self)
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We propose a set of transformation rules for first order formulae whose atoms are either equations between terms or "membership constraints" t 2 i. i can be interpreted as a regular tree language (i is called a sort in the algebraic specification community) or as a tree language in any class of languages which satisfies some adequate closure and decidability properties. This set of rules is proved to be correct, terminating and complete. This provides a quantifier elimination procedure: for every regular tree language L, the first order theory of some structure defining L is decidable. This extends the results of Mal'cev (1971), Maher (1988), Comon and Lescanne (1989). We also show how to apply our results to automatic inductive proofs in equational theories. Introduction To unify two terms s and t means to turn the equation s = t into an equivalent solved form which is either ? (this means that s = t has no solution, or, in other words, that s and t are not unifiable) or else a form...
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.
HigherOrder Matching and Tree Automata
 Proc. Conf. on Computer Science Logic
, 1997
"... ions x 1 : : : xn are assumed to have arity one. For instance, x 1 x 2 :c(x 3 :x 3 ; x 2 (x 1 )) (assumed in normal form) has the following representation as a tree: x 1 x 2 c \Gamma \Gamma @ @ x 3 x 2 x 3 x 1 In what follows, we assume that F is finite. This is not a restriction as, for countab ..."
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Cited by 25 (0 self)
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ions x 1 : : : xn are assumed to have arity one. For instance, x 1 x 2 :c(x 3 :x 3 ; x 2 (x 1 )) (assumed in normal form) has the following representation as a tree: x 1 x 2 c \Gamma \Gamma @ @ x 3 x 2 x 3 x 1 In what follows, we assume that F is finite. This is not a restriction as, for countably infinite alphabets, there is always another alphabet F 0 , which is finite, and an injective tree homomorphism h from T (F) into T (F) 0 such that h(T (F)) is recognizable by a finite tree automaton and the size of h(t) is linear with respect to the size of t. 1 However, for sake of clarity, we will keep the standard notations instead of using the encodings of F . 3.2 2automata We will use a slight modification of tree automata. The main difference with the definitions of [13, 4] is the presence of special symbols 2 ø which should be interpreted as any term of type ø . This slight modification is necessary because, for instance, the set of all closed terms is not recognizable by ...
Syntacticness, CycleSyntacticness and Shallow Theories
 INFORMATION AND COMPUTATION
, 1994
"... Solving equations in the free algebra T (F; X) (i.e. unification) uses the two rules: f(~s) = f( ~ t) ! ~s = ~ t (decomposition) and s[x] = x !? (occurcheck). These two rules are not correct in quotients of T (F; X) by a finitely generated congruence =E . Following C. Kirchner, we first define cl ..."
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Cited by 11 (0 self)
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Solving equations in the free algebra T (F; X) (i.e. unification) uses the two rules: f(~s) = f( ~ t) ! ~s = ~ t (decomposition) and s[x] = x !? (occurcheck). These two rules are not correct in quotients of T (F; X) by a finitely generated congruence =E . Following C. Kirchner, we first define classes of equational theories (called syntactic and cycle syntactic respectively) for which it is possible to derive some rules replacing the two above ones. Then, we show that these abstract classes are relevant: all shallow theories, i.e. theories which can be generated by equations in which variables occur at depth at most one, are both syntactic and cycle syntactic. Moreover, the new set of unification rules is terminating, which proves that unification is decidable and finitary in shallow theories. We give still further extensions. If the set of equivalence classes is infinite, a problem which turns out to be decidable in shallow theories, then shallow theories fulfill Colmerauer's indep...
Multiple counters automata, safety analysis and Presburger arithmetic
, 1998
"... . We consider automata with counters whose values are updated according to signals sent by the environment. A transition can be fired only if the values of the counters satisfy some guards (the guards of the transition). We consider guards of the form y i #y j + c i;j where y i is either x 0 i or ..."
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. We consider automata with counters whose values are updated according to signals sent by the environment. A transition can be fired only if the values of the counters satisfy some guards (the guards of the transition). We consider guards of the form y i #y j + c i;j where y i is either x 0 i or x i , the values of the counter i respectively after and before the transition, and # is any relational symbol in f=; ; ; ?; !g. We show that the set of possible counter values which can be reached after any number of iterations of a loop is definable in the additive theory of N (or Z or R depending on the type of the counters). This result can be used for the safety analysis of multiple counters automata. 1 Introduction Finite state automata provide a nice framework for the verification of reactive systems. Their main advantage is the equivalence between recognizability and definability in some decidable logic (e.g. Monadic Second Order Logic or some of its fragments such as temporal logi...
Results 1  10
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