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

On the Axiomatisability of Parallel Composition

This paper studies the existence of finite equational axiomatisations of the interleaving parallel composition operator modulo the behavioural equivalences in van Glabbeek's linear time-branching time spectrum. In the setting of the process algebra BCCSP over a finite set of actions, we provide finite, ground-complete axiomatisations for various simulation and (decorated) trace semantics. We also show that no congruence over BCCSP that includes bisimilarity and is included in possible futures equivalence has a finite, ground-complete axiomatisation; this negative result applies to all the nested trace and nested simulation semantics

(Bi)Simulations Up-to Characterise Process Semantics

We define (bi)simulations up-to a preorder and show how we can use them to provide a coinductive, (bi)simulation-like, characterisation of semantic (equivalences) preorders for processes. In particular, we can apply our results to all the semantics in the linear time-branching time spectrum that are defined by preorders coarser than the ready simulation preorder. The relation between bisimulations up-to and simulations up-to allows us to find some new relations between the equivalences that define the semantics and the corresponding preorders. In particular, we have shown that the simulation up-to an equivalence relation is a canonical preorder whose kernel is the given equivalence relation. Since all of these canonical preorders are defined in an homogeneous way, we can prove properties for them in a generic way. As an illustrative example of this technique, we generate an axiomatic characterisation of each of these canonical preorders, that is obtained simply by adding a single axiom to the axiomatization of the original equivalence relation. Thus we provide an alternative axiomatization for any axiomatizable preorder in the linear time-branching time spectrum, whose correctness and completeness can be proved once and for all. Although we first prove, by induction, our results for finite processes, then we see, by using continuity arguments, that they are also valid for infinite (finitary) processes

On the axiomatizability of ready traces, ready simulation and failure traces

Abstract. We provide an answer to an open question, posed by van Glabbeek [4], regarding the axiomatizability of ready trace semantics. We prove that if the alphabet of actions is finite, then there exists a (sound and complete) finite equational axiomatization for the process algebra BCCSP modulo ready trace semantics. We prove that if the alphabet is infinite, then such an axiomatization does not exist. Furthermore, we present finite equational axiomatizations for BCCSP modulo ready simulation and failure trace semantics, for arbitrary sets of actions.

On the Axiomatizability of Ready Traces, Ready Simulation, and Failure Traces

Fragments of mitochondrial DNA are known to get inserted into nuclear DNA to form NUMTs, i.e. nuclear pseudogenes of the mtDNA. The insertion of a NUMT is a rare event. Hundreds of pseudogenes have been cataloged in the human genome. NUMTs are, in essence, a special type of mutation with their own internal timer, which is synchronized with an established molecular clock, the mtDNA. Thus insertion of NUMTs can be timed with respect to evolution milestones such as the emergence of new species. We asked whether NUMTs were inserted uniformly over time or preferentially during certain periods of evolution, as implied by the "punctuated evolution" model. To our surprise, the NUMT insertion times do appear nonrandom with at least one cluster positioned at around 2.8 million years ago (Ma). Interestingly, 2.8Ma closely corresponds to the time of emergence of the genus Homo, and to a well-documented period of major climate change ca. 2.9-2.5Ma. It is tempting to hypothesize that the insertion of NUMTs is related to the speciation process. NUMTs could be either "riders", i.e., their insertion could be facilitated by the overall higher genome rearrangement activity during speciation, or "drivers", i.e. they may more readily get fixed in the population due to positive selection associated with speciation. If correct, the hypothesis would support the idea that evolution of our genus may have happened in a rapid, punctuated manner