A completeness theorem for Kleene algebras and the algebra of regular events
Papers presented at the IEEE symposium on Logic in computer science
On Hoare logic and Kleene algebra with tests
ACM Transactions on Computational Logic (TOCL)
Automata and Computability
Kleene Algebra with Tests: Completeness and Decidability
CSL '96 Selected Papers from the10th International Workshop on Computer Science Logic
Word problems requiring exponential time(Preliminary Report)
STOC '73 Proceedings of the fifth annual ACM symposium on Theory of computing
A Bialgebraic Approach to Automata and Formal Language Theory
LFCS '09 Proceedings of the 2009 International Symposium on Logical Foundations of Computer Science
| Hi-index | 0.00 |
In this paper, we develop the basic theory of disimulations, a type of relation between two automata which witnesses equivalence. We show that many standard constructions in the theory of automata such as determinization, minimization, inaccessible state removal, et al., are instances of disimilar automata. Then, using disimulations, we define an "algebraic" proof system for the equational theory of Kleene algebra in which a proof essentially consists of a sequence of matrices encoding automata and disimulations between them. We show that this proof system is complete for the equational theory of Kleene algebra, and that proofs in this system can be constructed by a PSPACE transducer.