Trace theory

Trace theory

In mathematics and computer science, trace theory aims to provide a concrete mathematical underpinning for the study of concurrent computation and process calculi. The underpining is provided by an algebraic definition of the free partially commutative monoid or trace monoid, or equivalently, the history monoid, which provides a concrete algebraic foundation, analogous to the way that the free monoid provides the underpining for formal languages.

The power of trace theory stems from the fact that the algebra of dependency graphs (such as Petri nets) is isomorphic to that of trace monoids, and thus, one can apply both algebraic formal language tools, as well as tools from graph theory.

Trace theory was first formulated by Antoni Mazurkiewicz in the 1970s, in an attempt to evade some of the problems in the theory of concurrent computation, including the problems of interleaving and non-deterministic choice with regards to refinement in process calculi.

References

* V. Diekert, G. Rozenberg, eds. "The Book of Traces", (1995) World Scientific, Singapore ISBN 9810220588
* Volker Diekert, Yves Metivier, " [http://citeseer.ist.psu.edu/diekert97partial.html Partial Commutation and Traces] ", In G. Rozenberg and A. Salomaa, editors, "Handbook of Formal Languages", Vol. 3, Beyond Words, pages 457--534. Springer-Verlag, Berlin, 1997.


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