In Rutten (2005), the theoretical basis was given for the synthesis of binary Mealy machines from specifications in 2-adic arithmetic. This construction is based on the symbolic computation of the coalgebraic notion of stream function derivative, a generalisation of the Brzozowski derivative of regular expressions. In this paper we complete the construction of Mealy machines from specifications in both 2-adic and modulo-2 arithmetic by describing how we decide equivalence of expressions via reduction to normal forms; we present a Haskell implementation of this Mealy synthesis algorithm; and a theoretical result which characterises the (number of) states in Mealy machines constructed from rational 2-adic specifications.
Elsevier B.V.
Electronic Notes in Theoretical Computer Science
Compositional Construction of Component Connectors
International Workshop on Coalgebraic Methods in Computer Science
Computer Security

Hansen, H., de Oliveira Costa, D., & Rutten, J. (2006). Synthesis of Mealy machines using derivatives. In Proceedings of the 8th Workshop on Coalgebraic Methods in Computer Science (pp. 27–45). Elsevier B.V.