Partial orders and fully abstract models for concurrency

In this thesis sets of labelled partial orders are employed as fundamental mathematical entities for modelling nondeterministic and concurrent processes thereby obtaining so-called noninterleaving semantics. Based on different closures of sets of labelled partial orders, simple algebraic languages are given denotational models fully abstract w.r.t. corresponding behaviourally motivated equivalences. Some of the equivalences are accompanied by adequate logics and sound axiomatisations of which one is complete

Foundations of Software Science and Computation Structures

This open access book constitutes the proceedings of the 24th International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2021, which was held during March 27 until April 1, 2021, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2021. The conference was planned to take place in Luxembourg and changed to an online format due to the COVID-19 pandemic. The 28 regular papers presented in this volume were carefully reviewed and selected from 88 submissions. They deal with research on theories and methods to support the analysis, integration, synthesis, transformation, and verification of programs and software systems

Pomsets and Unfolding of Reset Petri Nets

International audienceReset Petri nets are a particular class of Petri nets where transition firings can remove all tokens from a place without checking if this place actually holds tokens or not. In this paper we look at partial order semantics of such nets. In particular, we propose a pomset bisimulation for comparing their concurrent behaviours. Building on this pomset bisimulation we then propose a generalization of the standard finite complete prefixes of unfolding to the class of safe reset Petri nets

Posets with Interfaces for Concurrent Kleene Algebra

We introduce posets with interfaces (iposets) and generalise the serial composition of posets to a new gluing composition of iposets. In partial order semantics of concurrency, this amounts to designate events that continue their execution across components. Alternatively, in terms of decomposing concurrent systems, it allows cutting through some events, whereas serial composition may cut through edges only. We show that iposets under gluing composition form a category, extending the monoid of posets under serial composition, and a 2-category when enriched with a subsumption order and a suitable parallel composition as a lax tensor. This generalises the interchange monoids used in concurrent Kleene algebra. We also consider gp-iposets, which are generated from singletons by finitary gluing and parallel compositions. We show that the class includes the series-parallel posets as well as the interval orders, which are also well studied in concurrency theory. Finally, we show that not all posets are gp-iposets, exposing several posets that cannot occur as induced substructures of gp-iposets

The essence of bisimulation : a comparative study

The realm of approaches to operational descriptions and equivalences for concurrent systems in the literature leads to aseries of different attempts to give a uniform characterization of what should be considered as abisimulation, mostly in an algebraic and/or categorical framework. Meanwhile the realm of such approaches calls itselffor comparison and/or unification. We investigate how different abstract characterizations of bisimulations are related and how suitable they are to encompass the various concrete notions of bisimulation

Equivalence checking for weak bi-Kleene algebra

Pomset automata are an operational model of weak bi-Kleene algebra, which describes programs that can fork an execution into parallel threads, upon completion of which execution can join to resume as a single thread. We characterize a fragment of pomset automata that admits a decision procedure for language equivalence. Furthermore, we prove that this fragment corresponds precisely to series-rational expressions, i.e., rational expressions with an additional operator for bounded parallelism. As a consequence, we obtain a new proof that equivalence of series-rational expressions is decidable

Equivalence checking for weak bi-kleene algebra∗

Pomset automata are an operational model of weak bi-Kleene algebra, which describes programs that can fork an execution into parallel threads, upon completion of which execution can join to resume as a single thread. We characterize a fragment of pomset automata that admits a decision procedure for language equivalence. Furthermore, we prove that this fragment corresponds precisely to series-rational expressions, i.e., rational expressions with an additional operator for bounded parallelism. As a consequence, we obtain a new proof that equivalence of series-rational expressions is decidable