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

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

Mutual Mobile Membranes with Timers

A feature of current membrane systems is the fact that objects and membranes are persistent. However, this is not true in the real world. In fact, cells and intracellular proteins have a well-defined lifetime. Inspired from these biological facts, we define a model of systems of mobile membranes in which each membrane and each object has a timer representing their lifetime. We show that systems of mutual mobile membranes with and without timers have the same computational power. An encoding of timed safe mobile ambients into systems of mutual mobile membranes with timers offers a relationship between two formalisms used in describing biological systems

Logical Characterization of Bisimulation for Transition Relations over Probability Distributions with Internal Actions

In recent years the study of probabilistic transition systems has shifted to transition relations over distributions to allow for a smooth adaptation of the standard non-probabilistic apparatus. In this paper we study transition relations over probability distributions in a setting with internal actions. We provide new logics that characterize probabilistic strong, weak and branching bisimulation. Because these semantics may be considered too strong in the probabilistic context, Eisentraut et al. recently proposed weak distribution bisimulation. To show the flexibility of our approach based on the framework of van Glabbeek for the non-deterministic setting, we provide a novel logical characterization for the latter probabilistic equivalence as well

Rooted branching bisimulation as a congruence for probabilistic transition systems

Ponencia presentada en el 13 International Workshop on Quantitative Aspects of Programming Languages and Systems. London, United Kingdom, April 11-12, 2015.We propose a probabilistic transition system specification format, referred to as probabilistic RBB safe, for which rooted branching bisimulation is a congruence. The congruence theorem is based on the approach of Fokkink for the qualitative case. For this to work, the theory of transition system specifications in the setting of labeled transition systems needs to be extended to deal with probability distributions, both syntactically and semantically. We provide a scheduler-free characterization of probabilistic branching bisimulation as adapted from work of Andova et al. for the alternating model. Counter examples are given to justify the various conditions required by the format.Fil: Lee, Matías David. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina.Fil: De Vink, Erik P. Eindhoven University of Technology; The Netherlands.Fil: De Vink, Erik P. Centrum Wiskunde & Informatica; The Netherlands.Ciencias de la Computació

Quantifying the implicit process flow abstraction in SBGN-PD diagrams with Bio-PEPA

For a long time biologists have used visual representations of biochemical networks to gain a quick overview of important structural properties. Recently SBGN, the Systems Biology Graphical Notation, has been developed to standardise the way in which such graphical maps are drawn in order to facilitate the exchange of information. Its qualitative Process Diagrams (SBGN-PD) are based on an implicit Process Flow Abstraction (PFA) that can also be used to construct quantitative representations, which can be used for automated analyses of the system. Here we explicitly describe the PFA that underpins SBGN-PD and define attributes for SBGN-PD glyphs that make it possible to capture the quantitative details of a biochemical reaction network. We implemented SBGNtext2BioPEPA, a tool that demonstrates how such quantitative details can be used to automatically generate working Bio-PEPA code from a textual representation of SBGN-PD that we developed. Bio-PEPA is a process algebra that was designed for implementing quantitative models of concurrent biochemical reaction systems. We use this approach to compute the expected delay between input and output using deterministic and stochastic simulations of the MAPK signal transduction cascade. The scheme developed here is general and can be easily adapted to other output formalisms

Bisimulation by Partitioning Is ?((m+n)log n)

An asymptotic lowerbound of ?((m+n)log n) is established for partition refinement algorithms that decide bisimilarity on labeled transition systems. The lowerbound is obtained by subsequently analysing two families of deterministic transition systems - one with a growing action set and another with a fixed action set. For deterministic transition systems with a one-letter action set, bisimilarity can be decided with fundamentally different techniques than partition refinement. In particular, Paige, Tarjan, and Bonic give a linear algorithm for this specific situation. We show, exploiting the concept of an oracle, that the approach of Paige, Tarjan, and Bonic is not of help to develop a generic algorithm for deciding bisimilarity on labeled transition systems that is faster than the established lowerbound of ?((m+n)log n)