Logical Equations and Binary Relations: Interpretations in Logic Design and AI, Matrix Representation and Practically Efficient Algorithms for their Solution

A. Zakrevskij

Belarusian Academy of Science, Minsk, Belarus

Parallel researches are under progress concerning the problems of:

• representation of data and knowledge in systems of logical recognition,
• transforming data into knowledge (inductive inference),
• using the latter in procedures of logical recognition (deductive inference the type of theorem proving),
• representation of parallel algorithms of logical control (PALCs) and their verification,
• constructing and minimizing automata theory models and systems of Boolean functions realizing PALCs,
• logical design of AND/EXOR circuits implementing given Boolean functions and systems.

The common approach is suggested for solving these problems on the base of the theory of Boolean functions extended onto finite predicates, and on technique of logical equations and binary relations using matrix representation that was developed under research. Several methods for resolving the regarded problems were proposed, and practically efficient algorithms for finding optimal or suboptimal solutions of some basic combinatorial tasks were elaborated.

• Click here to return to my main page.
• Click here to go to the main page of the workshop.