In the paper, we introduce a new tree automata framework, called propositional tree automata, capturing the class of tree languages that are closed under an equational theory and Boolean operations. This framework originates in work on developing a su cient completeness checker for speci cations with rewriting modulo an equational theory. Propositional tree automata recognize regular equational...

Borgström et al. proposed a notion of symbolic bisimilarity for the Extended Spi Calculus [12]. They developed a prototype tool, called SBC (Symbolic Bisimulation Checker) [10] implementing observational equivalence checking for arbitrary processes using shared-key cryptography. However, it is based on hard-coded equational theories. We have partially extended SBC towards checking processes usi...

In AM93b] an asynchronous process algebra with multiple clocks, called PMC, was introduced and a complete axiomatization of strong bisimulation equivalence was given for a class of nite state processes. In this report we show how to extend the equational calculus so as to arrive at a complete axiomatization of observation congruence. Completeness is proven for the class of nite processes. With ...

Epigroups are semigroups equipped with an additional unary operation called pseudoinversion. Each finite semigroup can be considered as an epigroup. We prove the following theorem announced by Zhil’tsov in 2000: the equational theory of the class of all epigroups coincides with the equational theory of the class of all finite epigroups and is decidable. We show that the theory is not finitely b...

Epigroups are semigroups equipped with an additional unary operation called pseudoinversion. Each finite semigroup can be considered as an epigroup. We prove the following theorem announced by Zhil’tsov in 2000: the equational theory of the class of all epigroups coincides with the equational theory of the class of all finite epigroups and is decidable. We show that the theory is not finitely b...

Equational logic programming is an extended programming paradigm of equational programming. Central to the notion of equational logic programming is the problem of solving equations, which is also called unification in equational theories. In this paper, we investigate the problem of solving equations in O’Donnell’s equational language. We define an equality theory for this language which adequ...

We describe a new way to construct large subdirectly irreducibles within an equational class of algebras. We use this construction to show that there are forbidden geometries of multitraces for finite algebras in residually small equational classes. The construction is first applied to show that minimal equational classes generated by simple algebras of types 2, 3 or 4 are residually small if a...

The paper presents generalizations of results on so-called Horn logic, well-known in universal algebra, to the setting of fuzzy logic. The theories we consider consist of formulas which are implications between identities (equations) with premises weighted by truth degrees. We adopt Pavelka style: theories are fuzzy sets of formulas and we consider degrees of provability of formulas from theori...

Among the earliest publications of Evelyn Nelson are four papers which appeared in 1971—Nelson [1971a, 1971b] and Burris and Nelson [1971/72, 1971]. These papers contributed to our understanding of the intricate structural diversity of the lattice of equational theories. In particular, these papers revealed that large partition lattices occur as intervals in the lattice of equational theories o...