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

On the Two-Variable Fragment of the Equational Theory of the Max-Sum Algebra of the Natural Numbers

This paper shows that the collection of identities in two variables which hold in the algebra N of the natural numbers with constant zero, and binary operations of sum and maximum does not have a finite equational axiomatization. This gives an alternative proof of the non-existence of a finite basis for N - a result previously obtained by the authors. As an application of the main theorem, it is shown that the language of Basic Process Algebra (over a singleton set of actions), with or without the empty process, has no finite \omega-complete equational axiomatization modulo trace equivalence