Weak bisimilarity coalgebraically

We argue that weak bisimilarity of processes can be conveniently captured in a semantic domain by a combination of traces and coalgebraic finality, in such a way that important process algebra aspects such as parallel composition and recursion can be represented compositionally. We illustrate the usefulness of our approach by providing a fully-abstract denotational semantics for CCS under weak bisimilarity

Weak bisimilarity coalgebraically

We argue that weak bisimilarity of processes can be conveniently captured in a semantic domain by a combination of traces and coalgebraic finality, in such a way that important process algebra aspects such as parallel composition and recursion can be represented compositionally. We illustrate the usefulness of our approach by providing a fully-abstract denotational semantics for CCS under weak bisimilarity

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

On coalgebras with internal moves

In the first part of the paper we recall the coalgebraic approach to handling the so-called invisible transitions that appear in different state-based systems semantics. We claim that these transitions are always part of the unit of a certain monad. Hence, coalgebras with internal moves are exactly coalgebras over a monadic type. The rest of the paper is devoted to supporting our claim by studying two important behavioural equivalences for state-based systems with internal moves, namely: weak bisimulation and trace semantics. We continue our research on weak bisimulations for coalgebras over order enriched monads. The key notions used in this paper and proposed by us in our previous work are the notions of an order saturation monad and a saturator. A saturator operator can be intuitively understood as a reflexive, transitive closure operator. There are two approaches towards defining saturators for coalgebras with internal moves. Here, we give necessary conditions for them to yield the same notion of weak bisimulation. Finally, we propose a definition of trace semantics for coalgebras with silent moves via a uniform fixed point operator. We compare strong and weak bisimilation together with trace semantics for coalgebras with internal steps.Comment: Article: 23 pages, Appendix: 3 page

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 specification language for Reo connectors

Recent approaches to component-based software engineering employ coordinating connectors to compose components into software systems. Reo is a model of component coordination, wherein complex connectors are constructed by composing various type

Revisiting causality, coalgebraically

In this paper we recast the classical Darondeau–Degano’s causal semantics of concurrency in a coalgebraic setting, where we derive a compact model. Our construction is inspired by the one of Montanari and Pistore yielding causal automata, but we show that it is instance of an existing categorical framework for modeling the semantics of nominal calculi, whose relevance is further demonstrated. The key idea is to represent events as names, and the occurrence of a new event as name generation. We model causal semantics as a coalgebra over a presheaf, along the lines of the Fiore–Turi approach to the semantics of nominal calculi. More specifically, we take a suitable category of finite posets, representing causal relations over events, and we equip it with an endofunctor that allocates new events and relates them to their causes. Presheaves over this category express the relationship between processes and causal relations among the processes’ events. We use the allocation operator to define a category of well-behaved coalgebras: it models the occurrence of a new event along each transition. Then we turn the causal transition relation into a coalgebra in this category, where labels only exhibit maximal events with respect to the source states’ poset, and we show that its bisimilarity is essentially Darondeau–Degano’s strong causal bisimilarity. This coalgebra is still infinite-state, but we exploit the equivalence between coalgebras over a class of presheaves and History Dependent automata to derive a compact representation, where states only retain the poset of the most recent events for each atomic subprocess, and are isomorphic up to order-preserving permutations. Remarkably, this reduction of states is automatically performed along the equivalence

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