On the Degeneracy of Random Expressions Specified by Systems of Combinatorial Equations

Florent Koechlin (1) , Cyril Nicaud (1) , Pablo Rotondo (2)

1 LIGM - Laboratoire d'Informatique Gaspard-Monge
2 LITIS - Laboratoire d'Informatique, de Traitement de l'Information et des Systèmes

We consider general expressions, which are trees whose nodes are labeled with operators, that represent syntactic descriptions of formulas. We assume that there is an operator that has an absorbing pattern and prove that if we use this property to simplify a uniform random expression with n nodes, then the expected size of the result is bounded by a constant. In our framework, expressions are defined using a combinatorial system, which describes how they are built: one can ensure, for instance, that there are no two consecutive stars in regular expressions. This generalizes a former result where only one equation was allowed, confirming the lack of expressivity of uniform random expressions.

Domaines: Combinatoire [math.CO]; Théorie et langage formel [cs.FL]

Florent Koechlin, Cyril Nicaud, Pablo Rotondo. On the Degeneracy of Random Expressions Specified by Systems of Combinatorial Equations. International Conference on Developments in Language Theory (DLT 2020), May 2020, Tampa, United States. pp.164-177, ⟨10.1007/978-3-030-48516-0_13⟩. ⟨hal-03145943⟩