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2001
Springer

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

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Myhill-Nerode Relations on Automatic Systems and the Completeness of Kleene Algebra
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 restrictions. 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 using 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.
Dexter Kozen
Added 30 Jul 2010
Updated 30 Jul 2010
Type Conference
Year 2001
Where STACS
Authors Dexter Kozen
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