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Title: Myhill-Nerode Relations on Automatic Systems and the Completeness ofKleene Algebra
Authors: Kozen, Dexter
Keywords: computer science
technical report
Issue Date: 30-Nov-2000
Publisher: Cornell University
Abstract: 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.
Appears in Collections:Computer Science Technical Reports

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