Application of Information Relationships and Measures to Decomposition and Encoding of Incompletely Specified Sequential Machines

Modern circuit implementation technologies (FPGAs, CPLDs and complex gates) invalidate the traditional sequential synthesis methods. The new implementation platforms introduce new optimization criteria and implementation constraints the circuit optimization cannot be identified with the minimization of the number of terms or literals. It is necessary to perform the logic synthesis according to the new criteria and introduce an appropriate apparatus capable of effective manipulation in their domain. We propose to express the new criteria as the criteria of the optimized information flows — the information in the circuit being the realization of a given sequential machine is ordered according to its production and consumption; the information delivered to particular parts of the circuit is limited to the information relevant for computations performed in this part and is compressed on as few binary variables as possible. In this way, the interconnections are minimized and functions fed with compressed, relevant information have smaller input supports. Moreover, similar information is used and computed in the same part of the circuit, facilitating hardware reuse by constructing common sub-functions. This facilitates efficient FPGA, CPLD and complex gate implementation. Our approach necessitates usage of the appropriate information analysis apparatus — information relationships and measures. As an example of this new approach, we present in this paper application of the information flow analysis to the decompositional state encoding of sequential machines and the application of the information relationships and measures in this context. The presented experimental results confirm the effectiveness of this approach.