Elgot theories: A new perspective on the equational properties of iteration
Mathematical Structures in Computer Science
Context-free languages, coalgebraically
CALCO'11 Proceedings of the 4th international conference on Algebra and coalgebra in computer science
Sound and Complete Axiomatization of Trace Semantics for Probabilistic Systems
Electronic Notes in Theoretical Computer Science (ENTCS)
Well-Pointed coalgebras (extended abstract)
FOSSACS'12 Proceedings of the 15th international conference on Foundations of Software Science and Computational Structures
Sound and Complete Axiomatizations of Coalgebraic Language Equivalence
ACM Transactions on Computational Logic (TOCL)
A parameterized graph transformation calculus for finite graphs with monadic branches
Proceedings of the 15th Symposium on Principles and Practice of Declarative Programming
Electronic Notes in Theoretical Computer Science (ENTCS)
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Stream circuits are a convenient graphical way to represent streams (or stream functions) computed by finite dimensional linear systems. We present a sound and complete expression calculus that allows us to reason about the semantic equivalence of finite closed stream circuits. For our proof of the soundness and completeness we build on recent ideas of Bonsangue, Rutten and Silva. They have provided a "Kleene theorem'' and a sound and complete expression calculus for coalgebras for endofunctors of the category of sets. The key ingredient of the soundness and completeness proof is a syntactic characterization of the final locally finite coalgebra. In the present paper we extend this approach to the category of real vector spaces. We also prove that a final locally finite (dimensional) coalgebra is, equivalently, an initial iterative algebra. This makes the connection to existing work on the semantics of recursive specifications.