Abstract
Trace monoids are obtained from free monoids by defining a subset I of pairs of letters that are allowed to commute. Most of the work of this theory is an attempt to relate the properties of these monoids to the properties of I. Following the work initiated by Büchi we show that when I is an equivalence relation (the trace monoid is then a free product of free commutative monoids) it is possible to define a second order logic whose models are the traces viewed as dependence graphs and which characterizes exactly the sets of traces that are rational. This logic essentially utilizes a predicate based on the ordering defined by the dependence graph and a predicate related to a restricted use of the comparison of cardinality.
This research was supported by the PRC Mathématiques et Informatique
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Choffrut, C., Guerra, L. (1993). On the logical definability of some rational trace languages. In: Enjalbert, P., Finkel, A., Wagner, K.W. (eds) STACS 93. STACS 1993. Lecture Notes in Computer Science, vol 665. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56503-5_49
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DOI: https://doi.org/10.1007/3-540-56503-5_49
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