Information and Computation
Partial commutation and traces
Handbook of formal languages, vol. 3
The Book of Traces
Partial order semantics and read arcs
Theoretical Computer Science
Lectures on Petri Nets I: Basic Models, Advances in Petri Nets, the volumes are based on the Advanced Course on Petri Nets
Graph Theory with Applications to Engineering and Computer Science (Prentice Hall Series in Automatic Computation)
Projection Representation of Mazurkiewicz Traces
Fundamenta Informaticae - Concurrency Specification and Programming (CS&P)
Modelling concurrency with comtraces and generalized comtraces
Information and Computation
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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 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.