PMaude: Rewrite-based Specification Language for Probabilistic Object Systems

We introduce a rewrite-based specification language for modelling probabilistic concurrent and distributed systems. The language, based on PMaude, has both a rigorous formal basis and the characteristics of a high-level rule-based programming language. Furthermore, we provide tool support for performing discrete-event simulations of models written in PMaude, and for statistically analyzing various quantitative aspects of such models based on the samples that are generated through discrete-event simulation. Because distributed and concurrent communication protocols can be modelled using actors (concurrent objects with asynchronous message passing), we provide an actor PMaude module. The module aids writing specifications in a probabilistic actor formalism. This allows us to easily write specifications that are purely probabilistic - and not just non-deterministic. The absence of such (un-quantified) non-determinism in a probabilistic system is necessary for a form of statistical analysis that we also discuss. Specifically, we introduce a query language called Quantitative Temporal Expressions (or QuaTEx in short), to query various quantitative aspects of a probabilistic model. We also describe a statistical technique to evaluate QuaTEx expressions for a probabilistic model.

[1]  Gul Agha,et al.  A Protocol Description Language for Customizing Semantics. , 1994 .

[2]  DAVID G. KENDALL,et al.  Introduction to Mathematical Statistics , 1947, Nature.

[3]  José Meseguer,et al.  Specification and proof in membership equational logic , 2000, Theor. Comput. Sci..

[4]  José Meseguer,et al.  A logical theory of concurrent objects and its realization in the Maude language , 1993 .

[5]  MeseguerJosé.  Conditional rewriting logic as a unified model of concurrency , 1992 .

[6]  José Meseguer,et al.  Membership algebra as a logical framework for equational specification , 1997, WADT.

[7]  William J. Stewart,et al.  Introduction to the numerical solution of Markov Chains , 1994 .

[8]  Carolyn L. Talcott,et al.  A foundation for actor computation , 1997, Journal of Functional Programming.

[9]  Marco Ajmone Marsan,et al.  Modelling with Generalized Stochastic Petri Nets , 1995, PERV.

[10]  Gul Agha,et al.  Research directions in concurrent object-oriented programming , 1993 .

[11]  Mahesh Viswanathan,et al.  Statistical Model Checking of Black-Box Probabilistic Systems , 2004, CAV.

[12]  Marta Z. Kwiatkowska,et al.  PRISM: Probabilistic Symbolic Model Checker , 2002, Computer Performance Evaluation / TOOLS.

[13]  Gul Agha,et al.  Probabilistic Rewrite Theories: Unifying Models, Logics and Tools , 2003 .

[14]  Jane Hillston,et al.  A compositional approach to performance modelling , 1996 .

[15]  Joost-Pieter Katoen,et al.  The Modest Modeling Tool and Its Implementation , 2003, Computer Performance Evaluation / TOOLS.

[16]  Gul Agha,et al.  Formal Modeling and Analysis of DoS Using Probabilistic Rewrite Theories , 2005 .

[17]  Peter Csaba Ölveczky,et al.  Specification of real-time and hybrid systems in rewriting logic , 2002, Theor. Comput. Sci..

[18]  Bengt Jonsson,et al.  A logic for reasoning about time and reliability , 1990, Formal Aspects of Computing.

[19]  Gul A. Agha,et al.  A protocol description language for customizing failure semantics , 1994, Proceedings of IEEE 13th Symposium on Reliable Distributed Systems.

[20]  Mahesh Viswanathan,et al.  On Statistical Model Checking of Stochastic Systems , 2005, CAV.

[21]  Pedro R. D'Argenio,et al.  Algebras and Automata for Timed and Stochastic Systems , 1999 .

[22]  José Meseguer,et al.  A Rewriting Based Model for Probabilistic Distributed Object Systems , 2003, FMOODS.

[23]  Andrea Bianco,et al.  Model Checking of Probabalistic and Nondeterministic Systems , 1995, FSTTCS.

[24]  Martin L. Puterman,et al.  Markov Decision Processes: Discrete Stochastic Dynamic Programming , 1994 .

[25]  Kishor S. Trivedi,et al.  Stochastic Petri Net Models of Polling Systems , 1990, IEEE J. Sel. Areas Commun..

[26]  Koushik Sen,et al.  Rule-Based Runtime Verification , 2004, VMCAI.

[27]  Robert K. Brayton,et al.  Verifying Continuous Time Markov Chains , 1996, CAV.

[28]  Peter W. Glynn,et al.  On the role of generalized semi-Markov processes in simulation output analysis , 1983, WSC '83.

[29]  Joost-Pieter Katoen,et al.  Process algebra for performance evaluation , 2002, Theor. Comput. Sci..

[30]  Roberto Segala,et al.  Modeling and verification of randomized distributed real-time systems , 1996 .

[31]  Gul A. Agha,et al.  ACTORS - a model of concurrent computation in distributed systems , 1985, MIT Press series in artificial intelligence.

[32]  Robert K. Brayton,et al.  Model-checking continuous-time Markov chains , 2000, TOCL.

[33]  Gul A. Agha,et al.  Customization and composition of distributed objects: middleware abstractions for policy management , 1998, SIGSOFT '98/FSE-6.

[34]  Narciso Martí-Oliet,et al.  Maude: specification and programming in rewriting logic , 2002, Theor. Comput. Sci..

[35]  Jane Hillston,et al.  A Compositional Approach to Performance Modelling (Distinguished Dissertations in Computer Science) , 2005 .