Fundamenta Informaticae

We introduce a Timed Linda language (T-Linda) which is obtained by a natural timed interpretation of the usual constructs of the Linda model and by adding a simple primitive which allows one to specify time-outs. Parallel execution of processes follows the scheduling policy of interleaving, however maximal parallelism is assumed for actions depending on time. We first define the operational semantics of T-Linda by means of a transition system, then we define a denotational model which is based on timed reactive sequences. The correctness of this model is proved w.r.t. a notion of observables which includes finite traces of actions and input/output pairs.

A bottom-up investigation of algebraic structures corresponding to many valued logical systems is made. Particular attention is given to the unit interval as a prototypical model of these kind of structures. At the top level of our construction, Heyting Wajsberg algebras are defined and studied. The peculiarity of this algebra is the presence of two implications as primitive operators. This characteristic is helpful in the study of abstract rough approximations.

Several algebraic structures (namely HW, BZMV^dM, Stonean MV and MV_Δ algebras) related to many valued logical systems are considered and their equivalence is proved. Four propositional calculi whose Lindenbaum–Tarski algebra corresponds to the four equivalent algebraic structures are axiomatized and their semantical completeness is given.

In our paper we apply term rewriting to decidability of equations in classes of partial algebras, as well as to embeddability of partial algebras into classes of total ones. We follow the approach to partial algebras introduced by H.J. Kreowski in [13], in which (classes of) partial algebras are described by means of (classes of) total ones.

Actor-based modeling has been successfully applied to the representation of concurrent and distributed systems. Besides having an appropriate and efficient way for modeling these systems, one needs a formal verification approach for ensuring their correctness. In this paper, we develop an actor-based model for describing such systems, use temporal logic to specify properties of the model, and apply different abstraction and verification methods for verifying that the model meets its specification. We use a compositional verification approach for verifying safety properties of these models. For that we introduce a notion of component, based on an user-defined decomposition of the model. Components are more abstract than the model itself, and so we can reduce the state space of the model which makes it more amenable to model checking techniques. We prove that our abstraction technique preserves a set of behavioral specifications in temporal logic. The soundness of the abstraction is proved by the weak simulation relation between the constructs.