422 research outputs found
Conflict vs causality in event structures
Event structures are one of the best known models for concurrency. Many variants of the basic model and many possible notions of equivalence for them have been devised in the literature. In this paper, we study how the spectrum of equivalences for Labelled Prime Event Structures built by Van Glabbeek and Goltz changes if we consider two simplified notions of event structures: the first is obtained by removing the causality relation (Coherence Spaces) and the second by removing the conflict relation (Elementary Event Structures). As expected, in both cases the spectrum turns out to be simplified, since some notions of equivalence coincide in the simplified settings; actually, we prove that removing causality simplifies the spectrum considerably more than removing conflict. Furthermore, while the labeling of events and their cardinality play no role when removing causality, both the labeling function and the cardinality of the event set dramatically influence the spectrum of equivalences in the conflict-free setting
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
The Glory of the Past and Geometrical Concurrency
This paper contributes to the general understanding of the geometrical model
of concurrency that was named higher dimensional automata (HDAs) by Pratt. In
particular we investigate modal logics for such models and their expressive
power in terms of the bisimulation that can be captured. The geometric model of
concurrency is interesting from two main reasons: its generality and
expressiveness, and the natural way in which autoconcurrency and action
refinement are captured. Logics for this model, though, are not well
investigated, where a simple, yet adequate, modal logic over HDAs was only
recently introduced. As this modal logic, with two existential modalities,
during and after, captures only split bisimulation, which is rather low in the
spectrum of van Glabbeek and Vaandrager, the immediate question was what small
extension of this logic could capture the more fine-grained hereditary history
preserving bisimulation (hh)? In response, the work in this paper provides
several insights. One is the fact that the geometrical aspect of HDAs makes it
possible to use for capturing the hh-bisimulation, a standard modal logic that
does not employ event variables, opposed to the two logics (over less
expressive models) that we compare with. The logic that we investigate here
uses standard past modalities and extends the previously introduced logic
(called HDML) that had only forward, action-labelled, modalities. Besides, we
try to understand better the above issues by introducing a related model that
we call ST-configuration structures, which extend the configuration structures
of van Glabbeek and Plotkin. We relate this model to HDAs, and redefine and
prove the earlier results in the light of this new model. These offer a
different view on why the past modalities and geometrical concurrency capture
the hereditary history preserving bisimulation. Additional correlating insights
are also gained.Comment: 17 pages, 7 figure
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
Characterizing Behavioural Congruences for Petri Nets
We exploit a notion of interface for Petri nets in order to design a set of net combinators. For such a calculus of nets, we focus on the behavioural congruences arising from four simple notions of behaviour, viz., traces, maximal traces, step, and maximal step traces, and from the corresponding four notions of bisimulation, viz., weak and weak step bisimulation and their maximal versions. We characterize such congruences via universal contexts and via games, providing in such a way an understanding of their discerning powers
Place Bisimilarity is Decidable, Indeed!
Place bisimilarity is a behavioral equivalence for finite Petri nets,
proposed by Schnoebelen and co-workers in 1991. Differently from all the other
behavioral relations proposed so far, a place bisimulation is not defined over
the markings of a finite net, rather over its places, which are finitely many.
However, place bisimilarity is not coinductive, as the union of place
bisimulations may be not a place bisimulation. Place bisimilarity was claimed
decidable in [1], even if the algorithm used to this aim [2] does not
characterize this equivalence, rather the unique maximal place bisimulation
which is also an equivalence relation; hence, its decidability was not proved.
Here we show that it is possible to decide place bisimilarity with a simple,
yet inefficient, algorithm, which essentially scans all the place relations
(which are finitely many) to check whether they are place bisimulations.
Moreover, we propose a slightly coarser variant, we call d-place bisimilarity,
that we conjecture to be the coarsest equivalence, fully respecting causality
and branching time, to be decidable on finite Petri nets
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