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

Concurrent Constraint Calculi: a Declarative Paradigm for Modeling Music Systems.

Concurrent constraint programming (CCP) has emerged as a simple but powerful paradigm for concurrent systems; i.e. systems of multiple agents that interact with each other as for example in a collection of music processes (musicians) performing a particular piece. The ntcc calculus is a CCP formalism for modeling temporal reactive systems. In ntcc, processes can be constrained by temporal requirements such as delays, time-outs and pre-emptions. Thus, the calculus integrates two dimensions of computation: a horizontal dimension dealing with partial information (e.g., note > 60) and a vertical one in which temporal requirements come into play (e.g., a process must be executed at any time within the next ten time units). We shall show that the above integration is remarkably useful for modeling complex musical processes, in particular for music improvisation. For example, for the vertical dimension one can specify that a given process can nondeterministically choose any note satisfying a given constraint. For the horizontal dimension one can specify that the process can nondeterministically choose the time to play the note subject to a given time upper bound. This nondeterministic view is particularly suitable for processes representing a musician's choices when improvising. Similarly, the horizontal dimension may supply partial information on a rhythmic pattern that leaves room for variation while keeping a basic control. We shall also illustrate how implementing a weaker ntcc model of a musical process may greatly simplify the formal verification of its properties. We argue that this modeling strategy provides a "runnable specification" for music problems that eases the task of formally reasoning about them

On Zone-Based Analysis of Duration Probabilistic Automata

We propose an extension of the zone-based algorithmics for analyzing timed automata to handle systems where timing uncertainty is considered as probabilistic rather than set-theoretic. We study duration probabilistic automata (DPA), expressing multiple parallel processes admitting memoryfull continuously-distributed durations. For this model we develop an extension of the zone-based forward reachability algorithm whose successor operator is a density transformer, thus providing a solution to verification and performance evaluation problems concerning acyclic DPA (or the bounded-horizon behavior of cyclic DPA).Comment: In Proceedings INFINITY 2010, arXiv:1010.611

A Faster-Than Relation for Semi-Markov Decision Processes

When modeling concurrent or cyber-physical systems, non-functional requirements such as time are important to consider. In order to improve the timing aspects of a model, it is necessary to have some notion of what it means for a process to be faster than another, which can guide the stepwise refinement of the model. To this end we study a faster-than relation for semi-Markov decision processes and compare it to standard notions for relating systems. We consider the compositional aspects of this relation, and show that the faster-than relation is not a precongruence with respect to parallel composition, hence giving rise to so-called parallel timing anomalies. We take the first steps toward understanding this problem by identifying decidable conditions sufficient to avoid parallel timing anomalies in the absence of non-determinism.Comment: In Proceedings QAPL 2019, arXiv:2001.0616

NTCCRT: A concurrent constraint framework for soft-real time music interaction

Writing music interaction systems is not easy because their concurrent processes usually access shared resources in a non-deterministic order, often leading to unpredictable behavior. Using Pure Data (Pure Data) and Max/MSP, it is possible to program concurrency; however, it is difficult to synchronize processes based on multiple criteria. Process calculi such as the Non-deterministic Timed Concurrent Constraint (ntcc) calculus, overcome that problem by representing, declaratively, the synchronization of multiple criteria as constraints. In this article, we propose the framework Ntccrt, as a new alternative to manage concurrency in Pure Data and Max/MSP. Ntccrt is a real-time capable interpreter for ntcc. Using Ntccrt binary plugins in Pure Data, we executed models for machine improvisation and signal processing. We also analyzed two case studies: one of a machine improvisation system and one of a signal processing system. We found out that performance of both case studies is compatible with soft real-time music interaction; it means, a musician can interact with Ntccrt without noticeable delays during the interaction