Algebraic Structure of Combined Traces

Traces and their extension called combined traces (comtraces) are two formalmodels used in the analysis and verification of concurrent systems. Both modelsare based on concepts originating in the theory of formal languages, and theyare able to capture the notions of causality and simultaneity of atomic actionswhich take place during the process of a system's operation. The aim of thispaper is a transfer to the domain of comtraces and developing of somefundamental notions, which proved to be successful in the theory of traces. Inparticular, we introduce and then apply the notion of indivisible steps, thelexicographical canonical form of comtraces, as well as the representation of acomtrace utilising its linear projections to binary action subalphabets. Wealso provide two algorithms related to the new notions. Using them, one cansolve, in an efficient way, the problem of step sequence equivalence in thecontext of comtraces. One may view our results as a first step towards thedevelopment of infinite combined traces, as well as recognisable languages ofcombined traces.Comment: Short variant of this paper, with no proofs, appeared in Proceedings of CONCUR 2012 conferenc