Abstract
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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Buszkowski, W. (2006). On the Complexity of the Equational Theory of Relational Action Algebras. In: Schmidt, R.A. (eds) Relations and Kleene Algebra in Computer Science. RelMiCS 2006. Lecture Notes in Computer Science, vol 4136. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11828563_7
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DOI: https://doi.org/10.1007/11828563_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-37873-0
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