Algebraic Structure of Combined Traces

Traces and their extension called combined traces (comtraces) are two formal models used in the analysis and verification of concurrent systems. Both models are based on concepts originating in the theory of formal languages, and they are able to capture the notions of causality and simultaneity of atomic actions which take place during the process of a system's operation. The aim of this paper is a transfer to the domain of comtraces and developing of some fundamental notions, which proved to be successful in the theory of traces. In particular, we introduce and then apply the notion of indivisible steps, the lexicographical canonical form of comtraces, as well as the representation of a comtrace utilising its linear projections to binary action subalphabets. We also provide two algorithms related to the new notions. Using them, one can solve, in an efficient way, the problem of step sequence equivalence in the context of comtraces. One may view our results as a first step towards the development of infinite combined traces, as well as recognisable languages of combined traces.Comment: Short variant of this paper, with no proofs, appeared in Proceedings of CONCUR 2012 conferenc

A regular viewpoint on processes and algebra

While different algebraic structures have been proposed for the treatment of concurrency, finding solutions for equations over these structures needs to be worked on further. This article is a survey of process algebra from a very narrow viewpoint, that of finite automata and regular languages. What have automata theorists learnt from process algebra about finite state concurrency? The title is stolen from [31]. There is a recent survey article [7] on finite state processes which deals extensively with rational expressions. The aim of the present article is different. How do standard notions such as Petri nets, Mazurkiewicz trace languages and Zielonka automata fare in the world of process algebra? This article has no original results, and the attempt is to raise questions rather than answer them

A Model and Temporal Proof System for Networks of Processes

A model and a sound and complete proof system for networks of processes in which component processes communicate exclusively through messages is given. The model, an extension of the trace model, can desribe both synchronous and asynchronous networks. The proof system uses temporal-logic assertions on sequences of observations - a generalization of traces. The use of observations (traces) makes the proof system simple, compositional and modular, since internal details can be hidden. The expressive power of temporal logic makes it possible to prove temporal properties (safety, liveness, precedence, etc.) in the system. The proof system is language-independent and works for both synchronous and asynchronous networks