For polynomial set functors G, we introduce a language of expressions for describing elements of final G-coalgebra. We show that every state of a finite G-coalgebra corresponds to an expression in the language, in the sense that they both have the same semantics. Conversely, we give a compositional synthesis algorithm which transforms every expression into a finite G-coalgebra. The language of expressions is equipped with an equational system that is sound, complete and expressive with respect to G-bisimulation.
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Software Engineering [SEN]
Computer Security

Bonsangue, M.M, Rutten, J.J.M.M, & Silva, A.M. (2007). Regular expressions for polynomial coalgebras. Software Engineering [SEN]. CWI.