Myhill-Nerode Relations on Automatic Systems and the Completeness of Kleene Algebra

  • Dexter Kozen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2010)


It is well known that finite square matrices over a Kleene algebra again form a Kleene algebra. This is also true for infinite matrices under suitable restric- tions. One can use this fact to solve certain infinite systems of inequalities over a Kleene algebra. Automatic systems are a special class of infinite systems that can be viewed as infinite-state automata. Automatic systems can be collapsed us- ing Myhill-Nerode relations in much the same way that finite automata can. The Brzozowski derivative on an algebra of polynomials over a Kleene algebra gives rise to a triangular automatic system that can be solved using these methods. This provides an alternative method for proving the completeness of Kleene algebra.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Dexter Kozen
    • 1
  1. 1.Department of Computer ScienceCornell UniversityIthacaUSA

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