Solving of Regular Equations Revisited

  • Martin SulzmannEmail author
  • Kenny Zhuo Ming Lu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11884)


Solving of regular equations via Arden’s Lemma is folklore knowledge. We first give a concise algorithmic specification of all elementary solving steps. We then discuss a computational interpretation of solving in terms of coercions that transform parse trees of regular equations into parse trees of solutions. Thus, we can identify some conditions on the shape of regular equations under which resulting solutions are unambiguous. We apply our result to convert a DFA to an unambiguous regular expression. In addition, we show that operations such as subtraction and shuffling can be expressed via some appropriate set of regular equations. Thus, we obtain direct (algebraic) methods without having to convert to and from finite automaton.


Regular equations and expressions Parse trees Ambiguity Subtraction Shuffling 



We thank referees for CIAA’18, ICTAC’18 and ICTAC’19 for their helpful comments on previous versions of this paper.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Karlsruhe University of Applied SciencesKarlsruheGermany
  2. 2.Nanyang PolytechnicSingaporeSingapore

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