This paper provides a new, generalized approach to the problem of encoding information as vectors of binary digits. We furnish a formal definition for the  Boolean constrained encoding problem , and show that this definition encompasses many particular encoding problems found in VLSI design, at various description abstraction levels. Our approach can capture equivalence and/or compatibility classes in the original symbol set to encode, by allowing symbols codes to be cubes of a Boolean space, instead of the usual minterms. Besides, we introduce a unified framework to represent encoding constraints which is more general than previous efforts. The framework is based upon a new definition of the  pseudo-dichotomy  concept, and is adequate to guide the solution of encoding problems through the satisfaction of constraints extracted from the original problem statement. An encoding problem case study is presented, the state assignment of synchronous finite state machines with the simultaneous consideration of state minimization. The practical comparison with well-established approaches to solve this problem in two separate steps, shows that our solution is competitive with other published results. However, the case study is primarily intended to show the feasibility of the Boolean constrained encoding problem formulation.
['Ney Laert Vilar Calazans']
Boolean constrained encoding: a new formulation and a case study