A Rewriting Logic Approach to Stochastic and Spatial Constraint System Specification and Verification

This paper addresses the issue of specifying, simulating, and verifying reactive systems in rewriting logic. It presents an executable semantics for probabilistic, timed, and spatial concurrent constraint programming ---here called stochastic and spatial concurrent constraint systems (SSCC)--- in the rewriting logic semantic framework. The approach is based on an enhanced and generalized model of concurrent constraint programming (CCP) where computational hierarchical spaces can be assigned to belong to agents. The executable semantics faithfully represents and operationally captures the highly concurrent nature, uncertain behavior, and spatial and epistemic characteristics of reactive systems with flow of information. In SSCC, timing attributes ---represented by stochastic duration--- can be associated to processes, and exclusive and independent probabilistic choice is also supported. SMT solving technology, available from the Maude system, is used to realize the underlying constraint system of SSCC with quantifier-free formulas over integers and reals. This results in a fully executable real-time symbolic specification that can be used for quantitative analysis in the form of statistical model checking. The main features and capabilities of SSCC are illustrated with examples throughout the paper. This contribution is part of a larger research effort aimed at making available formal analysis techniques and tools, mathematically founded on the CCP approach, to the research community.Comment: arXiv admin note: text overlap with arXiv:1805.0743

Stochastic modelling of non Markovian Dynamics in Biochemical Reactions.

Biochemical reactions are often modelled as discrete-state continuous time stochastic processes evolving as memoryless Markov processes. However, in some cases, biochemical systems exhibit non-Markovian dynamics. We propose a methodology for building stochastic simulation algorithms which model accurately non-Markovian processes in some specific situations. Our methodology is based on and implemented in Concurrent Constraint Programming (CCP). Our technique allows us to randomly sample waiting times from probability density functions (PDFs) not necessarily distributed according to a negative exponential function. In this context, we discuss an important case-study in which the PDF for waiting times is inferred from single-molecule experiments. We show that, by relying on our methodology, it is possible to obtain accurate models of enzymatic reactions that, in specific cases, fit experimental data better than the corresponding Markovian models