A new theoretical formulation of the output encoding and state assignment targeting two-level logic implementations is presented.The formulation is based on a uniform representation of the input and output constraints.This allows to solve the input and output encoding problems, inherent in state assignment of FSM, simultaneously.The solution is based on the concept of dichotomy and graph coloring.

PHIFACT is a multi-level Boolean optimization program characterized by a controlled time-area trade-off. Its first phase, the Boolean phase, uses Boolean techniques of decomposition and merging to carry out a structural analysis and, in particular, to detect shared circuit parts. Its second phase, the restructuring phase, carries out a systematic exploration of the area-time design space by applying a user controlled sequence of transformations minimizing a parameterized cost function. The obtained results show the feasibility of full Boolean computations and open the way to an important family of new structural analysis techniques.>

PHIPLA, a new algorithm for logic minimization, is presented. The algorithm sets out to find optimal sum-of-products representations for a set of Boolean functions, thus contributing to area minimization of the Programmable Logic Array corresponding to the set of functions.

The problem of inserting an item in a list is frequently encountered in various application fields such as sorting, compiling, etc. It is shown that the insertion of an item in a list of N members may be realized at a cost proportional to N and within a delay proportional to log N.

Relates three classical concepts, viz. mixed radix number system, Kronecker product of matrices, and perfect shuffle. It presents an algebra which describes the hardware organization of the computation of a productMv, whereMis a matrix in Kronecker product form andvis a vector. The algebraic formalism describes both the blockwise structure of the computation and the various possible connection patterns.

Algebraic methods for designing multiple-valued I2L circuits are presented. A new operation, namely the truncated difference, is introduced and proved to be an efficient tool for both analyzing and synthesizing circuits.

Digital signal processing such as discrete Fourier transform requires complex number arithmetic. Number-theoretical properties favor odd-radix systems for simple implementation of complex number operations. An array ternary complex multiplier is presented and compared to other complex multipliers. As an illustration, a perfectly balanced ternary system is implemented by means of current-mode threshold logic gates.

Residue-based designs are shown to exist for a particular class of discrete functions called regular functions. If the design uses read-only memories (ROM's) only, it may be shown that the cost of the residue-based design may become significantly smaller than the cost of the straightforward tabular approach when the number of distinct function values is small with respect to the number of points in the definition domain.

After a brief outline of classical concepts relative to Boolean differential calculus, a theoretical study of the main differential operators is undertaken. Algebraic equations relating the classical concepts of prime implicants and of the discrete Fourier transform of a Boolean function to the differential operators are derived. Application of these concepts to several important problems arising in switching practice is mentioned.