2-Nested Simulation is not Finitely Equationally Axiomatizable

2-nested simulation was introduced by Groote and Vaandrager [10] as the coarsest equivalence included in completed trace equivalence for which the tyft/tyxt format is a congruence format. In the lineartime-branching time spectrum of van Glabbeek [8], 2-nested simulationis one of the few equivalences for which no finite equational axiomatization is presented. In this paper we prove that such an axiomatizationdoes not exist for 2-nested simulation.Keywords: Concurrency, process algebra, basic CCS, 2-nested simulation, equational logic, complete axiomatizations

Nested Semantics over Finite Trees are Equationally Hard

This paper studies nested simulation and nested trace semantics over the language BCCSP, a basic formalism to express finite process behaviour. It is shown that none of these semantics affords finite (in)equational axiomatizations over BCCSP. In particular, for each of the nested semantics studied in this paper, the collection of sound, closed (in)equations over a singleton action set is not finitely based

On the Existence of a Finite Base for Complete Trace Equivalence over BPA with Interrupt

We study Basic Process Algebra with interrupt modulo complete trace equivalence. We show that, unlike in the setting of the more demanding bisimilarity, a ground complete finite axiomatization exists. We explicitly give such an axiomatization, and extend it to a finite complete one in the special case when a single action is present

Bisimilarity is not Finitely Based over BPA with Interrupt

This paper shows that bisimulation equivalence does not afford a finite equational axiomatization over the language obtained by enriching Bergstra and Klop's Basic Process Algebra with the interrupt operator. Moreover, it is shown that the collection of closed equations over this language is also not finitely based

Continuous Additive Algebras and Injective Simulations of Synchronization Trees

The (in)equational properties of the least fixed point operation on(omega-)continuous functions on (omega-)complete partially ordered sets arecaptured by the axioms of (ordered) iteration algebras, or iterationtheories. We show that the inequational laws of the sum operation inconjunction with the least fixed point operation in continuous additivealgebras have a finite axiomatization over the inequations of orderediteration algebras. As a byproduct of this relative axiomatizability result, we obtain complete infinite inequational and finite implicationalaxiomatizations. Along the way of proving these results, we give a concrete description of the free algebras in the corresponding variety ofordered iteration algebras. This description uses injective simulations of regular synchronization trees. Thus, our axioms are also sound andcomplete for the injective simulation (resource bounded simulation) of(regular) processes.Keywords: equational logic, fixed points, synchronization trees, simulation