On completeness of omega-regular algebras

Authors:
Michael R. Laurence;Georg Struth
Affiliations:
Department of Computer Science, University of Sheffield, UK;Department of Computer Science, University of Sheffield, UK
Venue:
RAMiCS'12 Proceedings of the 13th international conference on Relational and Algebraic Methods in Computer Science
Year:
2012

Citing 12
Cited 0

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
Syntactic semigroups

Handbook of formal languages, vol. 1
Two Complete Axiom Systems for the Algebra of Regular Events

Journal of the ACM (JACM)
Separation and Reduction

MPC '00 Proceedings of the 5th International Conference on Mathematics of Program Construction
An Eilenberg Theorem for Infinity-Languages

ICALP '91 Proceedings of the 18th International Colloquium on Automata, Languages and Programming
Towards a refinement algebra

Science of Computer Programming - Special issue on mathematics of program construction (MPC 2002)
Partial, total and general correctness

MPC'10 Proceedings of the 10th international conference on Mathematics of program construction
Automated engineering of relational and algebraic methods in isabelle/hol

RAMICS'11 Proceedings of the 12th international conference on Relational and algebraic methods in computer science
Automating algebraic methods in isabelle

ICFEM'11 Proceedings of the 13th international conference on Formal methods and software engineering
An efficient coq tactic for deciding kleene algebras

ITP'10 Proceedings of the First international conference on Interactive Theorem Proving
Proof Pearl: Regular Expression Equivalence and Relation Algebra

Journal of Automated Reasoning

Quantified Score

Hi-index	0.00

Visualization

Abstract

Omega-regular algebras axiomatise the equational theory of omega-regular expressions as induced by omega-regular language identity. Wagner presented an omega-regular algebra which requires recursively defined side conditions in some of its axioms. We introduce a first-order Horn axiomatisation for which such conditions can be avoided because additive and multiplicative units are absent. We prove its completeness relative to Wagner's result using categorical constructions for adjoining additive and multiplicative units.