Logical Specification and Analysis of Fault Tolerant Systems through Partial Model Checking

This paper presents a framework for a logical characterisation of fault tolerance and its formal analysis based on partial model checking techniques. The framework requires a fault tolerant system to be modelled using a formal calculus, here the CCS process algebra. To this aim we propose a uniform modelling scheme in which to specify a formal model of the system, its failing behaviour and possibly its fault-recovering procedures. Once a formal model is provided into our scheme, fault tolerance - with respect to a given property - can be formalized as an equational µ-calculus formula. This formula expresses in a logic formalism, all the fault scenarios satisfying that fault tolerance property. Such a characterisation understands the analysis of fault tolerance as a form of analysis of open systems and thank to partial model checking strategies, it can be made independent on any particular fault assumption. Moreover this logical characterisation makes possible the fault-tolerance verification problem be expressed as a general µ-calculus validation problem, for solving which many theorem proof techniques and tools are available. We present several analysis methods showing the flexibility of our approach

Strong, Weak and Branching Bisimulation for Transition Systems and Markov Reward Chains: A Unifying Matrix Approach

We first study labeled transition systems with explicit successful termination. We establish the notions of strong, weak, and branching bisimulation in terms of boolean matrix theory, introducing thus a novel and powerful algebraic apparatus. Next we consider Markov reward chains which are standardly presented in real matrix theory. By interpreting the obtained matrix conditions for bisimulations in this setting, we automatically obtain the definitions of strong, weak, and branching bisimulation for Markov reward chains. The obtained strong and weak bisimulations are shown to coincide with some existing notions, while the obtained branching bisimulation is new, but its usefulness is questionable

Generalized Vietoris Bisimulations

We introduce and study bisimulations for coalgebras on Stone spaces [14]. Our notion of bisimulation is sound and complete for behavioural equivalence, and generalizes Vietoris bisimulations [4]. The main result of our paper is that bisimulation for a $\mathbf{Stone}$ coalgebra is the topological closure of bisimulation for the underlying $\mathbf{Set}$ coalgebra

Realizability Toposes from Specifications

We investigate a framework of Krivine realizability with I/O effects, and present a method of associating realizability models to specifications on the I/O behavior of processes, by using adequate interpretations of the central concepts of `pole' and `proof-like term'. This method does in particular allow to associate realizability models to computable functions. Following recent work of Streicher and others we show how these models give rise to triposes and toposes

Verifying P Systems with Costs by Using Priced-Timed Maude

We consider P systems that assigns storage costs per step to membranes, and execution costs to rules. We present an abstract syntax of the new class of membrane systems, and then deal with costs by extending the operational semantics of P systems with promoters, inhibitors and registers.We use Priced-Timed Maude to implement the P systems with costs. By using such a rewriting engine which corresponds to the semantics of membrane systems with costs, we are able to prove the operational correctness of this implementation. Based on such an operational correspondence, we can analyze properly the evolutions of the P systems with costs, and verify several reachability properties, including the cost of computations that reach a given membrane con guration. This approach opens the way to various optimization problems related to membrane systems, problems making sense in a bio-inspired model which now can be veri ed by using a complex software platform

Divergence-Preserving Branching Bisimilarity

This note considers the notion of divergence-preserving branching bisimilarity. It briefly surveys results pertaining to the notion that have been obtained in the past one-and-a-half decade, discusses its role in the study of expressiveness of process calculi, and concludes with some suggestions for future work.Comment: In Proceedings EXPRESS/SOS 2020, arXiv:2008.1241

A Branching Time Model of CSP

I present a branching time model of CSP that is finer than all other models of CSP proposed thus far. It is obtained by taking a semantic equivalence from the linear time - branching time spectrum, namely divergence-preserving coupled similarity, and showing that it is a congruence for the operators of CSP. This equivalence belongs to the bisimulation family of semantic equivalences, in the sense that on transition systems without internal actions it coincides with strong bisimilarity. Nevertheless, enough of the equational laws of CSP remain to obtain a complete axiomatisation for closed, recursion-free terms.Comment: Dedicated to Bill Roscoe, on the occasion of his 60th birthda