Lukasz Mikulski - Algebraic Structure of Combined Traces

lmcs:856 - Logical Methods in Computer Science, August 30, 2013, Volume 9, Issue 3 -
Algebraic Structure of Combined Traces

Authors: Lukasz Mikulski

    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.

    Volume: Volume 9, Issue 3
    Published on: August 30, 2013
    Accepted on: June 25, 2015
    Submitted on: January 14, 2013
    Keywords: Computer Science - Logic in Computer Science,Computer Science - Formal Languages and Automata Theory

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