Decidability of the equational theory of allegories

Decidability and Tameness in the Theory of Finite Semigroups

Combining Equational Tree Automata over AC and ACI Theories

In this paper, we study combining equational tree automata in two different senses: (1) whether decidability results about equational tree automata over disjoint theories E1 and E2 imply similar decidability results in the combined theory E1 ∪ E2; (2) checking emptiness of a language obtained from the Boolean combination of regular equational tree languages. We present a negative result for the...

Combining Algorithms for Deciding Knowledge in Security Protocols

In formal approaches, messages sent over a network are usually modeled by terms together with an equational theory, axiomatizing the properties of the cryptographic functions (encryption, exclusive or, . . . ). The analysis of cryptographic protocols requires a precise understanding of the attacker knowledge. Two standard notions are usually used: deducibility and indistinguishability. Those no...

And Damien Pous A

Kleene algebra axioms are complete with respect to both language models and binary relation models. In particular, two regular expressions recognise the same language if and only if they are universally equivalent in the model of binary relations. We consider Kleene allegories, i.e., Kleene algebras with two additional operations and a constant which are natural in binary relation models: inter...

On Equational Theories, Unification and Decidability

The following classes of equational theories, which are important in unification theory, are presented: permutative, finite, Noetherian, simple, almost collapse free, collapse free, regular, and ~-free theories. The relationships between the particular theories are shown and the connection between these classes and the unification hierarchy is pointed out. We give an equational theory that alwa...