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

TL;DR

This paper introduces an executable semantics for stochastic and spatial concurrent constraint systems (SSCC) within rewriting logic, enabling formal specification, simulation, and quantitative analysis of reactive systems with probabilistic, timed, and spatial features.

Contribution

It presents a novel, generalized model of concurrent constraint programming that incorporates hierarchical spatial information, stochastic timing, and probabilistic choices within rewriting logic.

Findings

Executable semantics accurately models concurrent, uncertain, and spatial behaviors.

Supports probabilistic timing and choice, enabling real-time statistical model checking.

Uses SMT solving in Maude for constraint solving over integers and reals.

Abstract

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.