Graphs Encoded by Regular Expressions

Author Stefan Gulan

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Stefan Gulan

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Stefan Gulan. Graphs Encoded by Regular Expressions. In 28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011). Leibniz International Proceedings in Informatics (LIPIcs), Volume 9, pp. 495-506, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)


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.
  • Digraphs
  • Regular Expressions
  • Finite Automata
  • Forbidden Minors


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