28 research outputs found
Characterising Testing Preorders for Finite Probabilistic Processes
In 1992 Wang & Larsen extended the may- and must preorders of De Nicola and
Hennessy to processes featuring probabilistic as well as nondeterministic
choice. They concluded with two problems that have remained open throughout the
years, namely to find complete axiomatisations and alternative
characterisations for these preorders. This paper solves both problems for
finite processes with silent moves. It characterises the may preorder in terms
of simulation, and the must preorder in terms of failure simulation. It also
gives a characterisation of both preorders using a modal logic. Finally it
axiomatises both preorders over a probabilistic version of CSP.Comment: 33 page
Real-Reward Testing for Probabilistic Processes (Extended Abstract)
We introduce a notion of real-valued reward testing for probabilistic
processes by extending the traditional nonnegative-reward testing with negative
rewards. In this richer testing framework, the may and must preorders turn out
to be inverses. We show that for convergent processes with finitely many states
and transitions, but not in the presence of divergence, the real-reward
must-testing preorder coincides with the nonnegative-reward must-testing
preorder. To prove this coincidence we characterise the usual resolution-based
testing in terms of the weak transitions of processes, without having to
involve policies, adversaries, schedulers, resolutions, or similar structures
that are external to the process under investigation. This requires
establishing the continuity of our function for calculating testing outcomes.Comment: In Proceedings QAPL 2011, arXiv:1107.074
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
Testing Reactive Probabilistic Processes
We define a testing equivalence in the spirit of De Nicola and Hennessy for
reactive probabilistic processes, i.e. for processes where the internal
nondeterminism is due to random behaviour. We characterize the testing
equivalence in terms of ready-traces. From the characterization it follows that
the equivalence is insensitive to the exact moment in time in which an internal
probabilistic choice occurs, which is inherent from the original testing
equivalence of De Nicola and Hennessy. We also show decidability of the testing
equivalence for finite systems for which the complete model may not be known
Rate-Based Transition Systems for Stochastic Process Calculi
A variant of Rate Transition Systems (RTS), proposed by Klin and Sassone, is introduced and used as the basic model for defining stochastic behaviour of processes. The transition relation used in our variant associates to each process, for each action, the set of possible futures paired with a measure indicating their rates. We show how RTS can be used for providing the operational semantics of stochastic extensions of classical formalisms, namely CSP and CCS. We also show that our semantics for stochastic CCS guarantees associativity of parallel composition. Similarly, in contrast with the original definition by Priami, we argue that a semantics for stochastic π-calculus can be provided that guarantees associativity of parallel composition
MarCaSPiS: a Markovian Extension of a Calculus for Services
Service Oriented Computing (SOC) is a design paradigm that has evolved from earlier paradigms including object-orientation and component-based software engineering. Important features of services are compositionality, context-independence, encapsulation and re-usability. To support the formal design and analysis of SOC applications recently a number of Service Oriented Calculi have been proposed. Most of them are based on process algebras enriched with primitives specific of service orientation such as operators for manipulating semi-structured data, mechanisms for describing safe client-service interactions, constructors for composing possibly unreliable services and techniques for services query and discovery. In this paper we show a versatile technique for the definition of Structural Operational Semantics of MarCaSPiS, a Markovian extension of one of such calculi, namely the Calculus of Sessions and Pipelines, CaSPiS. The semantics deals in an elegant way with a stochastic version of two-party synchronisation, typical of a service-oriented approach, and with the problem of transition multiplicity while preserving highly desirable mathematical properties such as associativity and commutativity of parallel composition.
We also show how the proposed semantics can be naturally used for defining a bisimulation-based behavioural equivalence for MarCaSPiS terms that induces the same equalities as those obtained via Strong Markovian Equivalence
The Power of Convex Algebras
Probabilistic automata (PA) combine probability and nondeterminism. They can
be given different semantics, like strong bisimilarity, convex bisimilarity, or
(more recently) distribution bisimilarity. The latter is based on the view of
PA as transformers of probability distributions, also called belief states, and
promotes distributions to first-class citizens.
We give a coalgebraic account of the latter semantics, and explain the
genesis of the belief-state transformer from a PA. To do so, we make explicit
the convex algebraic structure present in PA and identify belief-state
transformers as transition systems with state space that carries a convex
algebra. As a consequence of our abstract approach, we can give a sound proof
technique which we call bisimulation up-to convex hull.Comment: Full (extended) version of a CONCUR 2017 paper, to be submitted to
LMC