Graphs Encoded by Regular Expressions

Stefan Gulan (1)

1 Fachbereich IV - Informatik

In the conversion of finite automata to regular expressions, an exponential blowup in size can generally not be avoided. This is due to graph-structural properties of automata which cannot be directly encoded by regular expressions and cause the blowup combinatorially. In order to identify these structures, we generalize the class of arc-series-parallel digraphs to the acyclic case. The resulting digraphs are shown to be reversibly encoded by linear-sized regular expressions. We further derive a characterization of our new class by a finite set of forbidden minors and argue that these minors constitute the primitives causing the blowup in the conversion from automata to expressions.

Mots clés: Digraphs; Regular Expressions; Finite Automata; Forbidden Minors

Domaines: Complexité [cs.CC]; Algorithme et structure de données [cs.DS]

Stefan Gulan. Graphs Encoded by Regular Expressions. Symposium on Theoretical Aspects of Computer Science (STACS2011), Mar 2011, Dortmund, Germany. pp.495-506. ⟨hal-00573614⟩