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Uniform Random Expressions Lack Expressivity

Authors Florent Koechlin, Cyril Nicaud, Pablo Rotondo

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Florent Koechlin
  • Université Paris-Est, LIGM (UMR 8049), CNRS, ENPC, ESIEE, UPEM, France
Cyril Nicaud
  • Université Paris-Est, LIGM (UMR 8049), CNRS, ENPC, ESIEE, UPEM, France
Pablo Rotondo
  • Université Paris-Est, LIGM (UMR 8049), CNRS, ENPC, ESIEE, UPEM, France

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Florent Koechlin, Cyril Nicaud, and Pablo Rotondo. Uniform Random Expressions Lack Expressivity. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 51:1-51:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Discrete mathematics
  • Random expressions
  • simplification algorithms
  • analytic combinatorics


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