568 research outputs found
Branching Bisimilarity with Explicit Divergence
We consider the relational characterisation of branching bisimilarity with
explicit divergence. We prove that it is an equivalence and that it coincides
with the original definition of branching bisimilarity with explicit divergence
in terms of coloured traces. We also establish a correspondence with several
variants of an action-based modal logic with until- and divergence modalities
Computation Tree Logic with Deadlock Detection
We study the equivalence relation on states of labelled transition systems of
satisfying the same formulas in Computation Tree Logic without the next state
modality (CTL-X). This relation is obtained by De Nicola & Vaandrager by
translating labelled transition systems to Kripke structures, while lifting the
totality restriction on the latter. They characterised it as divergence
sensitive branching bisimulation equivalence.
We find that this equivalence fails to be a congruence for interleaving
parallel composition. The reason is that the proposed application of CTL-X to
non-total Kripke structures lacks the expressiveness to cope with deadlock
properties that are important in the context of parallel composition. We
propose an extension of CTL-X, or an alternative treatment of non-totality,
that fills this hiatus. The equivalence induced by our extension is
characterised as branching bisimulation equivalence with explicit divergence,
which is, moreover, shown to be the coarsest congruence contained in divergence
sensitive branching bisimulation equivalence
Folk Theorems on the Correspondence between State-Based and Event-Based Systems
Kripke Structures and Labelled Transition Systems are the two most prominent
semantic models used in concurrency theory. Both models are commonly believed
to be equi-expressive. One can find many ad-hoc embeddings of one of these
models into the other. We build upon the seminal work of De Nicola and
Vaandrager that firmly established the correspondence between stuttering
equivalence in Kripke Structures and divergence-sensitive branching
bisimulation in Labelled Transition Systems. We show that their embeddings can
also be used for a range of other equivalences of interest, such as strong
bisimilarity, simulation equivalence, and trace equivalence. Furthermore, we
extend the results by De Nicola and Vaandrager by showing that there are
additional translations that allow one to use minimisation techniques in one
semantic domain to obtain minimal representatives in the other semantic domain
for these equivalences.Comment: Full version of SOFSEM 2011 pape
Expressive Logics for Coinductive Predicates
The classical Hennessy-Milner theorem says that two states of an image-finite transition system are bisimilar if and only if they satisfy the same formulas in a certain modal logic. In this paper we study this type of result in a general context, moving from transition systems to coalgebras and from bisimilarity to coinductive predicates. We formulate when a logic fully characterises a coinductive predicate on coalgebras, by providing suitable notions of adequacy and expressivity, and give sufficient conditions on the semantics. The approach is illustrated with logics characterising similarity, divergence and a behavioural metric on automata
Characterising Probabilistic Processes Logically
In this paper we work on (bi)simulation semantics of processes that exhibit
both nondeterministic and probabilistic behaviour. We propose a probabilistic
extension of the modal mu-calculus and show how to derive characteristic
formulae for various simulation-like preorders over finite-state processes
without divergence. In addition, we show that even without the fixpoint
operators this probabilistic mu-calculus can be used to characterise these
behavioural relations in the sense that two states are equivalent if and only
if they satisfy the same set of formulae.Comment: 18 page
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
- …