The Kleene and the Parikh theorem in complete semirings
14th International Colloquium on Automata, languages and programming
A semiring on convex polygons and zero-sum cycle problems
SIAM Journal on Computing
The design and analysis of algorithms
The design and analysis of algorithms
A completeness theorem for Kleene algebras and the algebra of regular events
Papers presented at the IEEE symposium on Logic in computer science
Derivatives of Regular Expressions
Journal of the ACM (JACM)
Two Complete Axiom Systems for the Algebra of Regular Events
Journal of the ACM (JACM)
Automata and Computability
Introduction To Automata Theory, Languages, And Computation
Introduction To Automata Theory, Languages, And Computation
Semirings, Automata and Languages
Semirings, Automata and Languages
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Kleene Algebra withTests and Commutativity Conditions
TACAs '96 Proceedings of the Second International Workshop on Tools and Algorithms for Construction and Analysis of Systems
Dynamic algebras as a well-behaved fragment of relation algebras
Proceedings of the Conference on Algebraic Logic and Universal Algebra in Computer Science
Logic of Programs, Workshop
A decision procedure for bisimilarity of generalized regular expressions
SBMF'10 Proceedings of the 13th Brazilian conference on Formal methods: foundations and applications
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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.