André Thayse

P-functions: A new tool for the analysis and synthesis of binary programs

Considers the realization of switching functions by programs composed of certain conditional transfers (binary programs). Methods exist for optimizing binary trees, i.e. binary programs without reconvergent instructions. This paper studies methods for optimizing binary simple programs (programs with possible reconvergent instructions, but where a variable may be tested only once during a computation) and binary programs. The hardware implementations of these programs involve either multiplexers or demultiplexers and OR-gates.

From logic design to logic programming

The main purpose of the present book is to show that in the same way as P-functions can lead to algorithmic or imperative implementations via the algorithmic state machine model or via the parallel program schema, they can also lead to a declarative type of implementation via the theorem proving model. As P-functions are used for synthesizing algorithms, the result of the synthesis can be interpreted in terms of implementation tools. To the hardware, microprogrammed and programmed (in an algorithmic or imperative programming environment using fortran-like or pascal-like languages) implementations the authors can thus add logic programmed implementation as a possible result of the P-function calculus.

Universal algorithms for evaluating boolean functions

Abstract Theorems relating the most important concepts of switching theory to a new kind of difference operator are stated. This difference operator is then used as a unifying concept to solve, by means of a new type of algorithm, several problems arising in logical design.

Discrete function expansions in integer powers

Abstract This paper develops a method based on the Euclides algorithm for expanding a discrete function in terms of the successive powers of a given integer. We obtain as a particular case of this algorithm a new method for obtaining the binary expansion of a pseudo-Boolean function.