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

On Decidability of Persistence Notions

Abstract. Persistence is a widely investigated fundamental property of concurrent systems, which was extended in many ways. We propose a unified characterisation of several notions considered in the literature. The main result of the paper is a detailed description of a general and extendable framework that allows to state decision problems for different persistence notions (well known as well as newly formulated) and prove their decidability