Semirings, automata, languages
Semirings, automata, languages
Initiality, induction, and computability
Algebraic methods in semantics
The Kleene and the Parikh theorem in complete semirings
14th International Colloquium on Automata, languages and programming
Selected contributions on Trends, techniques, and problems in theoretical computer science. 4th International Meeting of Young Computer Scientists
On the decidability of some problems about rational subsets of free partially commutative monoids
Theoretical Computer Science
On Kleene algebras and closed semirings
MFCS '90 Proceedings on Mathematical foundations of computer science 1990
Dynamic algebras as a well-behaved fragment of relation algebras
AUSCRYPT '90 Proceedings of the international conference on cryptology on Advances in cryptology
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
Complete systems of B -rational identities
Theoretical Computer Science
A completeness theorem for Kleene algebras and the algebra of regular events
Papers presented at the IEEE symposium on Logic in computer science
Two Complete Axiom Systems for the Algebra of Regular Events
Journal of the ACM (JACM)
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
Logic of Programs, Workshop
The Complexity of Kleene Algebra with Tests
The Complexity of Kleene Algebra with Tests
Personalisation of web information systems - A term rewriting approach
Data & Knowledge Engineering
An algorithmic approach to high-level personalisation of web information systems
WAIM'05 Proceedings of the 6th international conference on Advances in Web-Age Information Management
On the representation of kleene algebras with tests
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
On the complexity of the equational theory of relational action algebras
RelMiCS'06/AKA'06 Proceedings of the 9th international conference on Relational Methods in Computer Science, and 4th international conference on Applications of Kleene Algebra
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We study the complexity of reasoning in Kleene algebra and *-continuous Kleene algebra in the presence of extra-equational assumptions E; that is, the complexity of deciding the validity of universal Horn formulas E → s = t, where E is a finite set of equations. We obtain various levels of complexity based on the form of the assumptions E. Our main results are as follows: for *-continuous Kleene algebra, (i) if E contains only commutativity assumptions pq = qp, the problem is Π10-complete; (ii) if E contains only monoid equations, the problem is Π20-complete; and (iii) for arbitrary equations E, the problem is Π11-complete. The last problem is the universal Horn theory of the *-continuous Kleene algebras. This resolves an open question of the author [D. Kozen, 1994, Inform. and Comput. 110, 366-390].