Deriving Syntax and Axioms for Quantitative Regular Behaviours
CONCUR 2009 Proceedings of the 20th International Conference on Concurrency Theory
Equational properties of iterative monads
Information and Computation
Subsequential transducers: a coalgebraic perspective
Information and Computation
Bisimulation proof methods in a path-based specification language for polynomial coalgebras
APLAS'10 Proceedings of the 8th Asian conference on Programming languages and systems
Quantitative Kleene coalgebras
Information and Computation
Elgot theories: A new perspective on the equational properties of iteration
Mathematical Structures in Computer Science
A decision procedure for bisimilarity of generalized regular expressions
SBMF'10 Proceedings of the 13th Brazilian conference on Formal methods: foundations and applications
Sound and Complete Axiomatization of Trace Semantics for Probabilistic Systems
Electronic Notes in Theoretical Computer Science (ENTCS)
A parameterized graph transformation calculus for finite graphs with monadic branches
Proceedings of the 15th Symposium on Principles and Practice of Declarative Programming
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Several dynamical systems, such as deterministic automata and labelled transition systems, can be described as coalgebras of so-called Kripke polynomial functors, built up from constants and identities, using product, coproduct and powerset. Locally finite Kripke polynomial coalgebras can be characterized up to bisimulation by a specification language that generalizes Kleene’s regular expressions for finite automata. In this paper, we equip this specification language with an axiomatization and prove it sound and complete with respect to bisimulation, using a purely coalgebraic argument. We demonstrate the usefulness of our framework by providing a finite equational system for (non-)deterministic finite automata, la-belled transition systems with explicit termination, and automata on guarded strings.