Abstract
Trace monoids are obtained from free monoids by defining a subsetI 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 ofI. Following the work initiated by Büchi we show that when the reflexive closure ofI is transitive (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 partial ordering defined by the dependence graph and a predicate related to a restricted use of the comparison of cardinality.
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This research was supported by the PRC Mathématiques et Informatique.
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Choffrut, C., Guerra, L. Logical definability of some rational trace languages. Math. Systems Theory 28, 397–420 (1995). https://doi.org/10.1007/BF01185864
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DOI: https://doi.org/10.1007/BF01185864