An algebraic and algorithmic method for analysing transition systems

Logiques temporelles basées sur actions pour la vérification des systèmes asynchrones

“…La logique de Dicky [Dic86] est un formalismeéquationnel -défini historiquement avant HmlR -conçu pour exprimer des propriétés temporelles sur les Ste. Cette logique comporte des primitives permettant de manipuler lesétats aussi bien que les transitions d'un Ste.…”

“…La logique de Dicky munie des opérateurs ci-dessus a une expressivité comparableà celle du µ-calcul modal ; en outre, elle autorise la description symétrique de propriétés portant sur le passé et sur le futur (un exemple d'opérateur du passé est Acc(X), qui caractérise lesétats ayant lesétats de X comme "ancêtres" dans le Ste). Enfin, l'opérateur Loop(X), dénotant lesétats présents sur les circuits du Ste qui passent par desétats satisfaisant X, est inexprimable en µ-calcul modal [Dic86].…”

Verification and comparison of transition systems

“…The logic CTL* can be defined in the same way, it has two sorts: states and paths, so that to be quite rigorous, it must contain two sets of logical operators, one for each sort, but the sort of such an operator can be determined from its context. As another example, we introduce the logic proposed by Dicky [12]. It has two sorts, states and transitions, denoted by a and r. it contains usual logical operators and constants, of both sorts, and the specific unary operators src and tgt of sort v ~ ~r, and in and out of sort a ~ r. Their interpretation in a transition system ,4 is and if R is the set of all transitions labeled by a, this is obviously equal to tile interpretation of (a).…”

MEC : a system for constructing and analysing transition systems

“…Given a formula F and a transition system .A, these systems compute the set F~t of states of A satisfying F (or, at least, decide if the "initial state" of .A belongs to F.a). In MEC we adopt a slightly different point of view, in some sense more algebraic than logical [7]. Let w be some logical operator and let F = w(F1,... ,Fn) be a formula.…”

“…It is well known that temporal logic operators can be characterized as least fixed points of equations [15,8,6], and this observation has led to the definition of the g-calculus as an extension of branching time temporal logics [13,11]. MEC provides for the definition of new operators characterized as least fixed points of systems of equations [7] and then its expressive power is at least as powerful as the expressive power of alternation-depth-one/z-calculus defined by Emerson and Lei [9]. Indeed these new operators defined by systems of equations are still computable in linear time, like the basic ones, because of the Arnold-CrubilM's algorithm [2] to solve fixed point equations.…”