9 research outputs found
Bisimulation of Labeled State-to-Function Transition Systems of Stochastic Process Languages
Labeled state-to-function transition systems, FuTS for short, admit multiple
transition schemes from states to functions of finite support over general
semirings. As such they constitute a convenient modeling instrument to deal
with stochastic process languages. In this paper, the notion of bisimulation
induced by a FuTS is proposed and a correspondence result is proven stating
that FuTS-bisimulation coincides with the behavioral equivalence of the
associated functor. As generic examples, the concrete existing equivalences for
the core of the process algebras ACP, PEPA and IMC are related to the
bisimulation of specific FuTS, providing via the correspondence result
coalgebraic justification of the equivalences of these calculi.Comment: In Proceedings ACCAT 2012, arXiv:1208.430
A Definition Scheme for Quantitative Bisimulation
FuTS, state-to-function transition systems are generalizations of labeled
transition systems and of familiar notions of quantitative semantical models as
continuous-time Markov chains, interactive Markov chains, and Markov automata.
A general scheme for the definition of a notion of strong bisimulation
associated with a FuTS is proposed. It is shown that this notion of
bisimulation for a FuTS coincides with the coalgebraic notion of behavioral
equivalence associated to the functor on Set given by the type of the FuTS. For
a series of concrete quantitative semantical models the notion of bisimulation
as reported in the literature is proven to coincide with the notion of
quantitative bisimulation obtained from the scheme. The comparison includes
models with orthogonal behaviour, like interactive Markov chains, and with
multiple levels of behavior, like Markov automata. As a consequence of the
general result relating FuTS bisimulation and behavioral equivalence we obtain,
in a systematic way, a coalgebraic underpinning of all quantitative
bisimulations discussed.Comment: In Proceedings QAPL 2015, arXiv:1509.0816
Coalgebraic Weak Bisimulation from Recursive Equations over Monads
Strong bisimulation for labelled transition systems is one of the most
fundamental equivalences in process algebra, and has been generalised to
numerous classes of systems that exhibit richer transition behaviour. Nearly
all of the ensuing notions are instances of the more general notion of
coalgebraic bisimulation. Weak bisimulation, however, has so far been much less
amenable to a coalgebraic treatment. Here we attempt to close this gap by
giving a coalgebraic treatment of (parametrized) weak equivalences, including
weak bisimulation. Our analysis requires that the functor defining the
transition type of the system is based on a suitable order-enriched monad,
which allows us to capture weak equivalences by least fixpoints of recursive
equations. Our notion is in agreement with existing notions of weak
bisimulations for labelled transition systems, probabilistic and weighted
systems, and simple Segala systems.Comment: final versio
Efficient Modelling and Generation of Markov Automata (extended version)
This paper introduces a framework for the efficient modelling and generation of Markov automata. It consists of (1) the data-rich process-algebraic language MAPA, allowing concise modelling of systems with nondeterminism, probability and Markovian timing; (2) a restricted form of the language, the MLPPE, enabling easy state space generation and parallel composition; and (3) several syntactic reduction techniques on the MLPPE format, for generating equivalent but smaller models. Technically, the framework relies on an encoding of MAPA into the existing prCRL language for probabilistic automata. First, we identify a class of transformations on prCRL that can be lifted to the Markovian realm using our encoding. Then, we employ this result to reuse prCRL's linearisation procedure to transform any MAPA specification to an equivalent MLPPE, and to lift three prCRL reduction techniques to MAPA. Additionally, we define two novel reduction techniques for MLPPEs. All our techniques treat data as well as Markovian and interactive behaviour in a fully symbolic manner, working on specifications instead of models and thus reducing state spaces prior to their construction. The framework has been implemented in our tool SCOOP, and a case study on polling systems and mutual exclusion protocols shows its practical applicability
Bisimulation of Labelled State-to-Function Transition Systems Coalgebraically
Labeled state-to-function transition systems, FuTS for short, are
characterized by transitions which relate states to functions of states over
general semirings, equipped with a rich set of higher-order operators. As such,
FuTS constitute a convenient modeling instrument to deal with process languages
and their quantitative extensions in particular. In this paper, the notion of
bisimulation induced by a FuTS is addressed from a coalgebraic point of view. A
correspondence result is established stating that FuTS-bisimilarity coincides
with behavioural equivalence of the associated functor. As generic examples,
the equivalences underlying substantial fragments of major examples of
quantitative process algebras are related to the bisimilarity of specific FuTS.
The examples range from a stochastic process language, PEPA, to a language for
Interactive Markov Chains, IML, a (discrete) timed process language, TPC, and a
language for Markov Automata, MAL. The equivalences underlying these languages
are related to the bisimilarity of their specific FuTS. By the correspondence
result coalgebraic justification of the equivalences of these calculi is
obtained. The specific selection of languages, besides covering a large variety
of process interaction models and modelling choices involving quantities,
allows us to show different classes of FuTS, namely so-called simple FuTS,
combined FuTS, nested FuTS, and general FuTS
A uniform definition of stochastic process calculi
We introduce a unifying framework to provide the semantics of process algebras, including their quantitative variants useful for modeling quantitative aspects of behaviors. The unifying framework is then used to describe some of the most representative stochastic process algebras. This
provides a general and clear support for an understanding of their similarities and differences. The framework is based on State to Function Labeled Transition Systems, FuTSs for short, that are state-transition structures where each transition is a triple of the form (s; Ī±;P). The first andthe second components are the source state, s, and the label, Ī±, of the transition, while the third component is the continuation function, P, associating a value of a suitable type to each state s0. For example, in the case of stochastic process algebras the value of the continuation function on s0 represents the rate of the negative exponential distribution characterizing the duration/delay of the action performed to reach state s0 from s. We first provide the semantics of a simple formalism used to describe Continuous-Time Markov Chains, then we model a number of process algebras that permit parallel composition of models according to the two main interaction paradigms (multiparty and one-to-one synchronization). Finally, we deal with formalisms where actions and rates are kept separate and address the issues related to the coexistence of stochastic, probabilistic, and non-deterministic behaviors. For each formalism, we establish the formal correspondence between the FuTSs semantics and its original semantics
Bisimulation of Labeled State-to-Function Transition Systems of Stochastic Process Languages
Abstract Labeled state-to-function transition systems, FuTS for short, admit multiple transition schemes from states to functions of finite support over general semirings. As such they constitute a convenient modeling instrument to deal with stochastic process languages. In this paper, the notion of bisimulation induced by a FuTS is addressed from a coalgebraic point of view. A correspondence result is proven stating that FuTS-bisimulation coincides with the behavioral equivalence of the associated functor. As generic examples, the concrete existing equivalences for the core of the stochastic process algebras PEPA and IML are related to the bisimulation of specific FuTS, providing via the correspondence result coalgebraic justification of the equivalences of these calculi.