On the Complexity of the Equational Theory of Relational Action Algebras

  • Wojciech Buszkowski
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4136)


Pratt [22] defines action algebras as Kleene algebras with residuals. In [9] it is shown that the equational theory of *-continuous action algebras (lattices) is Π\(^{0}_{1}\)–complete. Here we show that the equational theory of relational action algebras (lattices) is Π\(^{0}_{1}\) –hard, and some its fragments are Π\(^{0}_{1}\)–complete. We also show that the equational theory of action algebras (lattices) of regular languages is Π\(^{0}_{1}\)–complete.


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© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Wojciech Buszkowski
    • 1
  1. 1.Faculty of Mathematics and Computer Science, Adam Mickiewicz University in Poznań, Faculty of Mathematics and Computer ScienceUniversity of Warmia and Mazury in Olsztyn 

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