Reverse Bisimulations on Stable Configuration Structures

The relationships between various equivalences on configuration structures, including interleaving bisimulation (IB), step bisimulation (SB) and hereditary history-preserving (HH) bisimulation, have been investigated by van Glabbeek and Goltz (and later Fecher). Since HH bisimulation may be characterised by the use of reverse as well as forward transitions, it is of interest to investigate forms of IB and SB where both forward and reverse transitions are allowed. We give various characterisations of reverse SB, showing that forward steps do not add extra power. We strengthen Bednarczyk's result that, in the absence of auto-concurrency, reverse IB is as strong as HH bisimulation, by showing that we need only exclude auto-concurrent events at the same depth in the configuration

A Logic with Reverse Modalities for History-preserving Bisimulations

We introduce event identifier logic (EIL) which extends Hennessy-Milner logic by the addition of (1) reverse as well as forward modalities, and (2) identifiers to keep track of events. We show that this logic corresponds to hereditary history-preserving (HH) bisimulation equivalence within a particular true-concurrency model, namely stable configuration structures. We furthermore show how natural sublogics of EIL correspond to coarser equivalences. In particular we provide logical characterisations of weak history-preserving (WH) and history-preserving (H) bisimulation. Logics corresponding to HH and H bisimulation have been given previously, but not to WH bisimulation (when autoconcurrency is allowed), as far as we are aware. We also present characteristic formulas which characterise individual structures with respect to history-preserving equivalences.Comment: In Proceedings EXPRESS 2011, arXiv:1108.407

An Event Structure Model for Probabilistic Concurrent Kleene Algebra

We give a new true-concurrent model for probabilistic concurrent Kleene algebra. The model is based on probabilistic event structures, which combines ideas from Katoen's work on probabilistic concurrency and Varacca's probabilistic prime event structures. The event structures are compared with a true-concurrent version of Segala's probabilistic simulation. Finally, the algebraic properties of the model are summarised to the extent that they can be used to derive techniques such as probabilistic rely/guarantee inference rules.Comment: Submitted and accepted for LPAR19 (2013

A Logic for True Concurrency

We propose a logic for true concurrency whose formulae predicate about events in computations and their causal dependencies. The induced logical equivalence is hereditary history preserving bisimilarity, and fragments of the logic can be identified which correspond to other true concurrent behavioural equivalences in the literature: step, pomset and history preserving bisimilarity. Standard Hennessy-Milner logic, and thus (interleaving) bisimilarity, is also recovered as a fragment. We also propose an extension of the logic with fixpoint operators, thus allowing to describe causal and concurrency properties of infinite computations. We believe that this work contributes to a rational presentation of the true concurrent spectrum and to a deeper understanding of the relations between the involved behavioural equivalences.Comment: 31 pages, a preliminary version appeared in CONCUR 201

Back and forth bisimulations on prime event structures

SIGLEAvailable at INIST (FR), Document Supply Service, under shelf-number : 17660, issue : a.1992 n.888-I / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc

Über abstrakte Charakterisierungen von Bisimulation

Bisimulation wurde von Milner (1980) und Park (1981) auf Transitionssystemen eingefuehrt, um Prozesse zu identifizieren, die aus Sicht eines externen Beobachters nicht zu unterscheiden sind. Ausgehend von dieser Idee werden neue Bisimulationsbegriffe auch auf anderen Modellen parallelen Rechnens betrachtet, deren Definition von der Syntax her der urspruenglichen Definition von Bisimulation zumeist aehnlich sieht. Daraus erwaechst die Fragestellung: Was haben diese neuen Bisimulationen mit dem urspruenglichen Begriff zu tun, gibt es mehr als einen nur syntaktischen Zusammenhang zwischen ihnen, laesst sich ein gemeinsamer Ueberbegriff, eine abstrakte Charakterisierung finden? In der Literatur finden sich verschiedene Ansaetze fuer eine abstrakte Charakterisierung von Bisimulation: Degano, De Nicola und Montanari (1993) verwenden spezielle Baeume, Malacaria (1995) arbeitet mit Methoden der Algebra, Aczel und Mendler (1989) einerseits und Joyal, Nielsen und Winskel (1994) andereseits nutzen Begriffe der Kategorientheorie. Wir vergleichen in dieser Arbeit die beiden letztgenannten Ansaetze. Zum einen suchen wir nach direkten Zusammenhaengen zwischen den abstrakten Charakterisierungen. Zum anderen fragen wir uns, ob sich konkrete Bisimulationen auf unterschiedlichen Modellen parallelen Rechnens mittels der abstrakten Charakterisierungen darstellen lassen. Beide Vergleiche lassen den Schluss zu, dass die Charakterisierung von Aczel von den untersuchten Konzepten das umfassendste ist. Von daher beantworten wir die Frage, was eine Bisimulation ist, mit dem Begriff der AM-Bisimulation: Eine Bisimulation zwischen zwei Objekten ist ein Transitionssystem, welches das beobachtbare "Verhalten" wiedergibt, das beiden Objekten gemeinsam ist

Algebraic Verification of Probabilistic and Concurrent Systems

This thesis provides an algebraic modelling and verification of probabilistic concurrent systems in the style of Kleene algebra. Without concurrency, it is shown that the equational theory of continuous probabilistic Kleene algebra is complete with respect to an automata model under standard simulation equivalence. This yields a minimisation-based decision procedure for the algebra. Without probability, an event structure model of Hoare et al.'s concurrent Kleene algebra is constructed. These two algebras are then ``merged" to provide probabilistic concurrent Kleene algebra which is used to discover and prove development rules for probabilistic concurrent systems (e.g. rely/guarantee calculus). Soundness of the new algebra is ensured by models based on probabilistic automata (interleaving) and probabilistic bundle event structures (true concurrency) quotiented with the respective simulation equivalences. Lastly, event structures with implicit probabilities are constructed to provide a state based model for the soundness of the probabilistic rely/guarantee rules