The Reversible Temporal Process Language

Reversible debuggers help programmers to quickly find the causes of misbehaviours in concurrent programs. These debuggers can be founded on the well-studied theory of causal-consistent reversibility, which allows one to undo any action provided that its consequences are undone beforehand. Till now, causal-consistent reversibility never considered time, a key aspect in real world applications. Here, we study the interplay between reversibility and time in concurrent systems via a process algebra. The Temporal Process Language (TPL) by Hennessy and Regan is a well-understood extension of CCS with discrete-time and a timeout operator. We define revTPL, a reversible extension of TPL, and we show that it satisfies the properties expected from a causal-consistent reversible calculus. We show that, alternatively, revTPL can be interpreted as an extension of reversible CCS with time

The Reversible Temporal Process Language

Reversible debuggers help programmers to quickly find the causes of misbehaviours in concurrent programs. These debuggers can be founded on the well-studied theory of causal-consistent reversibility, which allows one to undo any action provided that its consequences are undone beforehand. Till now, causal-consistent reversibility never considered time, a key aspect in real world applications. Here, we study the interplay between reversibility and time in concurrent systems via a process algebra. The Temporal Process Language (TPL) by Hennessy and Regan is a well-understood extension of CCS with discrete-time and a timeout operator. We define revTPL, a reversible extension of TPL, and we show that it satisfies the properties expected from a causal-consistent reversible calculus. We show that, alternatively, revTPL can be interpreted as an extension of reversible CCS with time

A general conservative extension theorem in process algebras with inequalities

We prove a general conservative extension theorem for transition system based process theories with easy-to-check and reasonable conditions. The core of this result is another general theorem which gives sufficient conditions for a system of operational rules and an extension of it in order to ensure conservativity, that is, provable transitions from an original term in the extension are the same as in the original system. As a simple corollary of the conservative extension theorem we prove a completeness theorem. We also prove a general theorem giving sufficient conditions to reduce the question of ground confluence modulo some equations for a large term rewriting system associated with an equational process theory to a small term rewriting system under the condition that the large system is a conservative extension of the small one. We provide many applications to show that our results are useful. The applications include (but are not limited to) various real and discrete time settings in ACP, ATP, and CCS and the notions projection, renaming, stage operator, priority, recursion, the silent step, autonomous actions, the empty process, divergence, etc

The Absolute Relativity Theory

This paper is a first presentation of a new approach of physics that we propose to refer as the Absolute Relativity Theory (ART) since it refutes the idea of a pre-existing space-time. It includes an algebraic definition of particles, interactions and Lagrangians. It proposed also a purely algebraic explanation of the passing of time phenomenon that leads to see usual Euler-Lagrange equations as the continuous version of the Knizhnik-Zamolodchikov monodromy. The identification of this monodromy with the local ones of the Lorentzian manifolds gives the Einstein equation algebraically explained in a quantized context. A fact that could lead to the unification of physics. By giving an algebraic classification of particles and interactions, the ART also proposes a new branch of physics, namely the Mass Quantification Theory, that provides a general method to calculate the characteristics of particles and interactions. Some examples are provided. The MQT also predicts the existence of as of today not yet observed particles that could be part of the dark matter. By giving a new interpretation of the weak interaction, it also suggests an interpretation of the so-called dark energy

Levy Processes and Quasi-Shuffle Algebras

We investigate the algebra of repeated integrals of semimartingales. We prove that a minimal family of semimartingales generates a quasi-shuffle algebra. In essence, to fulfill the minimality criterion, first, the family must be a minimal generator of the algebra of repeated integrals generated by its elements and by quadratic covariation processes recursively constructed from the elements of the family. Second, recursively constructed quadratic covariation processes may lie in the linear span of previously constructed ones and of the family, but may not lie in the linear span of repeated integrals of these. We prove that a finite family of independent Levy processes that have finite moments generates a minimal family. Key to the proof are the Teugels martingales and a strong orthogonalization of them. We conclude that a finite family of independent Levy processes form a quasi-shuffle algebra. We discuss important potential applications to constructing efficient numerical methods for the strong approximation of stochastic differential equations driven by Levy processes.Comment: 10 page

A formal methodology for the verification of concurrent systems

There is an increasing emphasis on the use of software to control safety critical plants for a wide area of applications. The importance of ensuring the correct operation of such potentially hazardous systems points to an emphasis on the verification of the system relative to a suitably secure specification. However, the process of verification is often made more complex by the concurrency and real-time considerations which are inherent in many applications. A response to this is the use of formal methods for the specification and verification of safety critical control systems. These provide a mathematical representation of a system which permits reasoning about its properties. This thesis investigates the use of the formal method Communicating Sequential Processes (CSP) for the verification of a safety critical control application. CSP is a discrete event based process algebra which has a compositional axiomatic semantics that supports verification by formal proof. The application is an industrial case study which concerns the concurrent control of a real-time high speed mechanism. It is seen from the case study that the axiomatic verification method employed is complex. It requires the user to have a relatively comprehensive understanding of the nature of the proof system and the application. By making a series of observations the thesis notes that CSP possesses the scope to support a more procedural approach to verification in the form of testing. This thesis investigates the technique of testing and proposes the method of Ideal Test Sets. By exploiting the underlying structure of the CSP semantic model it is shown that for certain processes and specifications the obligation of verification can be reduced to that of testing the specification over a finite subset of the behaviours of the process