Symbolic Synthesis of Mealy Machines from Arithmetic Bitstream Functions - H.H. Hansen; J. Rutten (Scientific Annals of Computer Science, 2010)
In this paper, we describe a symbolic synthesis method which given an algebraic expression that specifies a bitstream function f, constructs a (minimal) Mealy machine that realises f. The synthesis algorithm can be seen as an analogue of Brzozowski's construction of a finite deterministic automaton from a regular expression. It is based on a coinductive characterisation of the operators of 2-adic arithmetic in terms of stream differential equations.