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Decomposition of TrPTL formulas

By Raphael Meyer and Antoine Petit


Partial orders based verifications methods are now well developed. In this framework, several suitable logics have already been defined. We focus on this paper on the logic TrPTL, as defined by Thiagarajan, for which models are the well known (infinite) Mazurkiewicz traces. We study the case where the alphabet is not connected. Our main theoretical result is that any TrPTL formula can be decomposed in an effective way as the disjunction of formulas on the connected components. Note that this result can be viewed as a direct logical counterpart of the famous Mezei's theorem on recognizable sets in a direct product of free monoids. Finally, we show that our result can also be of practical interest. Precisely, we exhibit families of formulas for which the use of our decomposition procedure decreases the complexity of the decision procedure of satisfiability

Year: 1997
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