196 research outputs found
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 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
Hennessy-Milner Theorems via Galois Connections
We introduce a general and compositional, yet simple, framework that allows to derive soundness and expressiveness results for modal logics characterizing behavioural equivalences or metrics (also known as Hennessy-Milner theorems). It is based on Galois connections between sets of (real-valued) predicates on the one hand and equivalence relations/metrics on the other hand and covers a part of the linear-time-branching-time spectrum, both for the qualitative case (behavioural equivalences) and the quantitative case (behavioural metrics). We derive behaviour functions from a given logic and give a condition, called compatibility, that characterizes under which conditions a logically induced equivalence/metric is induced by a fixpoint equation. In particular, this framework allows to derive a new fixpoint characterization of directed trace metrics
A tutorial on interactive Markov chains
Interactive Markov chains (IMCs) constitute a powerful sto- chastic model that extends both continuous-time Markov chains and labelled transition systems. IMCs enable a wide range of modelling and analysis techniques and serve as a semantic model for many industrial and scientific formalisms, such as AADL, GSPNs and many more. Applications cover various engineering contexts ranging from industrial system-on-chip manufacturing to satellite designs. We present a survey of the state-of-the-art in modelling and analysis of IMCs.\ud
We cover a set of techniques that can be utilised for compositional modelling, state space generation and reduction, and model checking. The significance of the presented material and corresponding tools is highlighted through multiple case studies
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
(Metric) Bisimulation Games and Real-Valued Modal Logics for Coalgebras
Behavioural equivalences can be characterized via bisimulations, modal logics and spoiler-defender games. In this paper we review these three perspectives in a coalgebraic setting, which allows us to generalize from the particular branching type of a transition system. We are interested in qualitative notions (classical bisimulation) as well as quantitative notions (bisimulation metrics).
Our first contribution is to introduce a spoiler-defender bisimulation game for coalgebras in the classical case. Second, we introduce such games for the metric case and furthermore define a real-valued modal coalgebraic logic, from which we can derive the strategy of the spoiler. For this logic we show a quantitative version of the Hennessy-Milner theorem
Retracing some paths in categorical semantics: From process-propositions-as-types to categorified reals and computers
The logical parallelism of propositional connectives and type constructors
extends beyond the static realm of predicates, to the dynamic realm of
processes. Understanding the logical parallelism of process propositions and
dynamic types was one of the central problems of the semantics of computation,
albeit not always clear or explicit. It sprung into clarity through the early
work of Samson Abramsky, where the central ideas of denotational semantics and
process calculus were brought together and analyzed by categorical tools, e.g.
in the structure of interaction categories. While some logical structures borne
of dynamics of computation immediately started to emerge, others had to wait,
be it because the underlying logical principles (mainly those arising from
coinduction) were not yet sufficiently well-understood, or simply because the
research community was more interested in other semantical tasks. Looking back,
it seems that the process logic uncovered by those early semantical efforts
might still be starting to emerge and that the vast field of results that have
been obtained in the meantime might be a valley on a tip of an iceberg.
In the present paper, I try to provide a logical overview of the gamut of
interaction categories and to distinguish those that model computation from
those that capture processes in general. The main coinductive constructions
turn out to be of this latter kind, as illustrated towards the end of the paper
by a compact category of all real numbers as processes, computable and
uncomputable, with polarized bisimulations as morphisms. The addition of the
reals arises as the biproduct, real vector spaces are the enriched
bicompletions, and linear algebra arises from the enriched kan extensions. At
the final step, I sketch a structure that characterizes the computable fragment
of categorical semantics.Comment: 63 pages, 40 figures; cut two words from the title, tried to improve
(without lengthening) Sec.8; rewrote a proof in the Appendi
On bisimulation and model-checking for concurrent systems with partial order semantics
EP/G012962/1In concurrency theory—the branch of (theoretical) computer science that studies the logical
and mathematical foundations of parallel computation—there are two main formal ways of
modelling the behaviour of systems where multiple actions or events can happen independently
and at the same time: either with interleaving or with partial order semantics.
On the one hand, the interleaving semantics approach proposes to reduce concurrency to the
nondeterministic, sequential computation of the events the system can perform independently.
On the other hand, partial order semantics represent concurrency explicitly by means of an
independence relation on the set of events that the system can execute in parallel; following
this approach, the so-called ‘true concurrency’ approach, independence or concurrency is a
primitive notion rather than a derived concept as in the interleaving framework.
Using interleaving or partial order semantics is, however, more than a matter of taste. In
fact, choosing one kind of semantics over the other can have important implications—both
from theoretical and practical viewpoints—as making such a choice can raise different issues,
some of which we investigate here. More specifically, this thesis studies concurrent systems
with partial order semantics and focuses on their bisimulation and model-checking problems;
the theories and techniques herein apply, in a uniform way, to different classes of Petri nets,
event structures, and transition system with independence (TSI) models.
Some results of this work are: a number of mu-calculi (in this case, fixpoint extensions of
modal logic) that, in certain classes of systems, induce exactly the same identifications as some
of the standard bisimulation equivalences used in concurrency. Secondly, the introduction of
(infinite) higher-order logic games for bisimulation and for model-checking, where the players
of the games are given (local) monadic second-order power on the sets of elements they are
allowed to play. And, finally, the formalization of a new order-theoretic concurrent game
model that provides a uniform approach to bisimulation and model-checking and bridges some
mathematical concepts in order theory with the more operational world of games.
In particular, we show that in all cases the logic games for bisimulation and model-checking
developed in this thesis are sound and complete, and therefore, also determined—even when
considering models of infinite state systems; moreover, these logic games are decidable in the
finite case and underpin novel decision procedures for systems verification.
Since the mu-calculi and (infinite) logic games studied here generalise well-known fixpoint
modal logics as well as game-theoretic decision procedures for analysing concurrent systems
with interleaving semantics, this thesis provides some of the groundwork for the design of a
logic-based, game-theoretic framework for studying, in a uniform manner, several concurrent
systems regardless of whether they have an interleaving or a partial order semantics
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