Concurrency, sigma-algebras and probabilistic fairness

International audienceWe give an interpretation through sigma-algebras of phenomena encountered in concurrency theory when dealing with "infinite confusion"--the extreme opposite of confusion-free event structures. The set of runs of a safe Petri net is equipped with its Borel sigma-algebra F. The fine structure of F describes the complexity of choices along runs, and we show that a transfinite induction of finite degree is needed to explore all choices of runs in general. The degree is minimal (zero) when confusion is bounded, corresponding to the classes of confusion free and locally finite event structures. We relate this construction to probabilistic fairness by showing how to randomize the net equipped with its Borel sigma-algebra by using only the first step of our decomposition, and making it thus more effective. Hence the serious difficulty brought by the above transfiniteness in the application of Kolmogorov extension theorem is bypassed thanks to probabilistic fairnes

A method for designing asynchronous probabilistic processes

25 pagesWe present a method for constructing asynchronous probabilistic processes. The asynchronous probabilistic processes thus obtained are called invariant. They generalize the familiar independent and identically distributed sequences of random variables to an asynchronous framework. Invariant processes are shown to be characterised by a finite family of real numbers, their characteristic numbers. Our method provides first a way to obtaining necessary and sufficient normalization conditions for a finite family of real numbers to be the characteristic numbers of some invariant asynchronous probabilistic process; and second, a procedure for constructing new asynchronous probabilistic processes

Probabilistic Process Algebra

Every day we witness the fast development of the hardware and software technology. This, of course, is the reason that new and more complex systems controlled by some kind of computational-based devices become an unseparated part of our daily life. As more as the system complexity increases, as more the reasoning about its correct behaviour becomes dif??cult. A variety of consequences may occur as a result of a failure, ranging from simple annoying to life threatening ones. Thus for some systems it is crucial that they exhibit a correct functioning. However, for systems with an extremely complex construction it is almost impossible to give an absolute guarantee for their correctness. In this case, it is still satisfactory to know that the possibility for a system to fail is low enough. Formal methods have been developed for establishing correctness of computer systems. They provide rigorous methods with which one can formally specify properties of a systems's intended behaviour, and also can check if the system conforms to that speci??cation. In case of complex systems we need a formal method that allows us to reason in compositional way, it provides us with techniques that can be used to build larger systems from the composition of smaller ones. Process algebra carries exactly this idea; it provides operators that allow to compose processes in order to obtain a more complex process. Besides, every process algebra contains a set of axioms. Every axiom is an algebraic equation that carries our intuition and insight in process behaviour, it expresses which two processes behaviour we consider equal. In such a way, manipulation with processes becomes manipulation with equations in the algebraic sense. But, equations and operators do not have any meaning unless we place them in a certain real ¿world¿ and match the terms of the process algebra with the entities of the real world. This step is traditionally called ¿giving a semantic of the syntax¿. The structure constructed in this way is called a model of the considered process algebra. For every given process algebra we can construct an in??nite number of models, but only several of them are interesting for the purpose process algebra was developed as a formal method. However, there is a tendency always to use so-called a bisimulation model. In this thesis we propose several process algebras and construct their models based on the notion of bisimulation

A formal framework for the specification of interactive systems

We are primarily concerned with interactive systems whose behaviour is highly reliant on end user activity. A framework for describing and synthesising such systems is developed. This consists of a functional description of the capabilities of a system together with a means of expressing its desired 'usability'. Previous work in this area has concentrated on capturing 'usability properties' in discrete mathematical models. We propose notations for describing systems in a 'requirements' style and a 'specification' style. The requirements style is based on a simple temporal logic and the specification style is based on Lamport's Temporal Logic of Actions (TLA) [74]. System functionality is specified as a collection of 'reactions', the temporal composition of which define the behaviour of the system. By observing and analysing interactions it is possible to determine how 'well' a user performs a given task. We argue that a 'usable' system is one that encourages users to perform their tasks efficiently (i.e. to consistently perform their tasks well) hence a system in which users perform their tasks well in a consistent manner is likely to be a usable system. The use of a given functionality linked with different user interfaces then gives a means by which interfaces (and other aspects) can be compared and suggests how they might be harnessed to bias system use so as to encourage the desired user behaviour. Normalising across different users anq different tasks moves us away from the discrete nature of reactions and hence to comfortably describe the use of a system we employ probabilistic rather than discrete mathematics. We illustrate that framework with worked examples and propose an agenda for further work

Strategic Port Graph Rewriting: an Interactive Modelling Framework

International audienceWe present strategic port graph rewriting as a basis for the implementation of visual modelling tools. The goal is to facilitate the specification and programming tasks associated with the modelling of complex systems. A system is represented by an initial graph and a collection of graph rewrite rules, together with a user-defined strategy to control the application of rules. The traditional operators found in strategy languages for term rewriting have been adapted to deal with the more general setting of graph rewriting, and some new constructs have been included in the strategy language to deal with graph traversal and management of rewriting positions in the graph. We give a formal semantics for the language, and describe its implementation: the graph transformation and visualisation tool Porgy

Programming and symbolic computation in Maude

[EN] Rewriting logic is both a flexible semantic framework within which widely different concurrent systems can be naturally specified and a logical framework in which widely different logics can be specified. Maude programs are exactly rewrite theories. Maude has also a formal environment of verification tools. Symbolic computation is a powerful technique for reasoning about the correctness of concurrent systems and for increasing the power of formal tools. We present several new symbolic features of Maude that enhance formal reasoning about Maude programs and the effectiveness of formal tools. They include: (i) very general unification modulo user-definable equational theories, and (ii) symbolic reachability analysis of concurrent systems using narrowing. The paper does not focus just on symbolic features: it also describes several other new Maude features, including: (iii) Maude's strategy language for controlling rewriting, and (iv) external objects that allow flexible interaction of Maude object-based concurrent systems with the external world. In particular, meta-interpreters are external objects encapsulating Maude interpreters that can interact with many other objects. To make the paper self-contained and give a reasonably complete language overview, we also review the basic Maude features for equational rewriting and rewriting with rules, Maude programming of concurrent object systems, and reflection. Furthermore, we include many examples illustrating all the Maude notions and features described in the paper.Duran has been partially supported by MINECO/FEDER project TIN2014-52034-R. Escobar has been partially supported by the EU (FEDER) and the MCIU under grant RTI2018-094403-B-C32, by the Spanish Generalitat Valenciana under grant PROMETE0/2019/098, and by the US Air Force Office of Scientific Research under award number FA9550-17-1-0286. MartiOliet and Rubio have been partially supported by MCIU Spanish project TRACES (TIN2015-67522-C3-3-R). Rubio has also been partially supported by a MCIU grant FPU17/02319. Meseguer and Talcott have been partially supported by NRL Grant N00173 -17-1-G002. Talcott has also been partially supported by ONR Grant N00014-15-1-2202.Durán, F.; Eker, S.; Escobar Román, S.; NARCISO MARTÍ OLIET; José Meseguer; Rubén Rubio; Talcott, C. (2020). Programming and symbolic computation in Maude. Journal of Logical and Algebraic Methods in Programming. 110:1-58. https://doi.org/10.1016/j.jlamp.2019.100497S158110Alpuente, M., Escobar, S., Espert, J., & Meseguer, J. (2014). A modular order-sorted equational generalization algorithm. 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Symbolic reachability analysis using narrowing and its application to verification of cryptographic protocols. Higher-Order and Symbolic Computation, 20(1-2), 123-160. doi:10.1007/s10990-007-9000-6C. Olarte, E. Pimentel, C. Rocha, Proving structural properties of sequent systems in rewriting logic, in: [121], 2018, pp. 115–135.Ölveczky, P. C., & Meseguer, J. (2007). Semantics and pragmatics of Real-Time Maude. Higher-Order and Symbolic Computation, 20(1-2), 161-196. doi:10.1007/s10990-007-9001-5Ölveczky, P. C., & Thorvaldsen, S. (2009). Formal modeling, performance estimation, and model checking of wireless sensor network algorithms in Real-Time Maude. Theoretical Computer Science, 410(2-3), 254-280. doi:10.1016/j.tcs.2008.09.022Rocha, C., Meseguer, J., & Muñoz, C. (2017). Rewriting modulo SMT and open system analysis. Journal of Logical and Algebraic Methods in Programming, 86(1), 269-297. doi:10.1016/j.jlamp.2016.10.001Şerbănuţă, T. F., Roşu, G., & Meseguer, J. (2009). A rewriting logic approach to operational semantics. Information and Computation, 207(2), 305-340. doi:10.1016/j.ic.2008.03.026Skeirik, S., & Meseguer, J. (2018). Metalevel algorithms for variant satisfiability. Journal of Logical and Algebraic Methods in Programming, 96, 81-110. doi:10.1016/j.jlamp.2017.12.006S. Skeirik, A. Ştefănescu, J. Meseguer, A constructor-based reachability logic for rewrite theories, in: [61], 2018, pp. 201–217.Strachey, C. (2000). Higher-Order and Symbolic Computation, 13(1/2), 11-49. doi:10.1023/a:1010000313106A. Ştefănescu, S. Ciobâcă, R. Mereuta, B.M. Moore, T. Serbanuta, G. Roşu, All-path reachability logic, in: [36], 2014, pp. 425–440.Tushkanova, E., Giorgetti, A., Ringeissen, C., & Kouchnarenko, O. (2015). A rule-based system for automatic decidability and combinability. Science of Computer Programming, 99, 3-23. doi:10.1016/j.scico.2014.02.00