The analysis of security protocols requires precise formulations of the knowledge of protocol participants and attackers. In formal approaches, this knowledge is often treated in terms of message deducibility and indistinguishability relations. In this paper we study the decidability of these two relations. The messages in question may employ functions (encryption, decryption, etc.) axiomatized...

In this paper we present the ITP/OCL tool, a rewritingbased tool that supports automatic validation of UML static class diagrams with respect to OCL invariants. From a conceptual point of view, the ITP/OCL tool is directly based on the equational specification of UML+OCL class diagrams developed in [11], according to which: i) class and object diagrams are specified as membership equational the...

Equational theories underly many elds of computing, including functional programming, symbolic algebra, theorem proving, term rewriting and constraint solving. In this paper we show a method for implementing many equational theories with a limited class of logic programs. We de ne regular equational theories, a useful class of theories, and illustrate with a number of examples how our method ca...

We establish some relations between the class of truth-equational logics, the class of assertional logics, other classes in the Leibniz hierarchy, and the classes in the Frege hierarchy. We argue that the class of assertional logics belongs properly in the Leibniz hierarchy. We give two new characterizations of truth-equational logics in terms of their full generalized models, and use them to o...

This paper focuses on the equational class S„ of Brouwerian algebras and the equational class L„ of Heyting algebras generated by an »-element chain. Firstly, duality theories are developed for these classes. Next, the projectives in the dual categories are determined, and then, by applying the dualities, the injectives and absolute subretracts in Sn and L„ are characterized. Finally, free prod...

We present a method for mass proofs of theorems of certain forms in a formal theory of fuzzy relations and classes. The method is based on formal identification of fuzzy classes and inner truth values with certain fuzzy relations, which allows transferring basic properties of sup-T and inf-R compositions to a family of more than 30 composition-related operations, including sup-T and inf-R image...

We present a method for mass proofs of theorems of certain forms in a formal theory of fuzzy relations and classes. The method is based on formal identification of fuzzy classes and inner truth values with certain fuzzy relations, which allows transferring basic properties of sup-T and inf-R compositions to a family of more than 30 composition-related operations, including sup-T and inf-R image...

Among others we will see that the equational theory of ! dimensional rep-resentable polyadic equality algebras (RPEA ! 's) is not schema axiomatizable. This result is in interesting contrast with the Daigneault-Monk representation theorem, which states that the class of representable polyadic algebras is nite schema-axiomatizable (and hence the equational theory of this class is nite schema-axi...

This paper gives an equational axiomatization of probabilistic bisimulation equivalence for a class of finite-state agents previously studied by Stark and Smolka ((2000) Proof, Language, and Interaction: Essays in Honour of Robin Milner, pp. 571–595). The axiomatization is obtained by extending the general axioms of iteration theories (or iteration algebras), which characterize the equational p...

The multiplicity of formalisms and corresponding verification systems makes the transformation useful for interoperations among them. We have proposed an approach to the transformation of state machines from a syntax-constrained class of equational theories into rewrite theories, which can be verified by Maude’s model checking facilities. However, the efficiency of model checking generated rewr...