A completeness theorem for Kleene algebras and the algebra of regular events
Papers presented at the IEEE symposium on Logic in computer science
Two Families of Languages Related to ALGOL
Journal of the ACM (JACM)
A New Normal-Form Theorem for Context-Free Phrase Structure Grammars
Journal of the ACM (JACM)
Universal coalgebra: a theory of systems
Theoretical Computer Science - Modern algebra and its applications
Decidability of DPDA equivalence
Theoretical Computer Science
An Introduction To Formal Languages And Automata
An Introduction To Formal Languages And Automata
Automata and Coinduction (An Exercise in Coalgebra)
CONCUR '98 Proceedings of the 9th International Conference on Concurrency Theory
Towards Kleene Algebra with Recursion
CSL '91 Proceedings of the 5th Workshop on Computer Science Logic
Behavioural differential equations: a coinductive calculus of streams, automata, and power series
Theoretical Computer Science
Formal languages and their relation to automata
Formal languages and their relation to automata
A Sound and Complete Calculus for Finite Stream Circuits
LICS '10 Proceedings of the 2010 25th Annual IEEE Symposium on Logic in Computer Science
Context-free languages via coalgebraic trace semantics
CALCO'05 Proceedings of the First international conference on Algebra and Coalgebra in Computer Science
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We give a coalgebraic account of context-free languages using the functor D(X) = 2 × XA for deterministic automata over an alphabet A, in three different but equivalent ways: (i) by viewing context-free grammars as D-coalgebras; (ii) by defining a format for behavioural differential equations (w.r.t. D) for which the unique solutions are precisely the context-free languages; and (iii) as the D-coalgebra of generalized regular expressions in which the Kleene star is replaced by a unique fixed point operator. In all cases, semantics is defined by the unique homomorphism into the final coalgebra of all languages, paving the way for coinductive proofs of context-free language equivalence. Furthermore, the three characterizations can serve as the basis for the definition of a general coalgebraic notion of context-freeness, which we see as the ultimate long-term goal of the present study.