Uniform Random Expressions Lack Expressivity

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

1 LIGM - Laboratoire d'Informatique Gaspard-Monge

In this article, we question the relevance of uniform random models for algorithms that use expressions as inputs. Using a general framework to describe expressions, we prove that if there is a subexpression that is absorbing for a given operator, then, after repeatedly applying the induced simplification to a uniform random expression of size n, we obtain an equivalent expression of constant expected size. This proves that uniform random expressions lack expressivity, as soon as there is an absorbing pattern. For instance, (a + b) is absorbing for the union for regular expressions on {a, b}, hence random regular expressions can be drastically reduced using the induced simplification.

Mots clés: random expressions; simplification algorithms; analytic combinatorics

Domaines: Théorie et langage formel [cs.FL]

Florent Koechlin, Cyril Nicaud, Pablo Rotondo. Uniform Random Expressions Lack Expressivity. MFCS 2019, Aug 2019, Aachen, Germany. pp.51:1-51:14, ⟨10.4230/LIPIcs.MFCS.2019.51⟩. ⟨hal-03145930⟩