Technology independent optimization when implementing sparse systems of disjunctive normal forms of Boolean functions in ASIC

Abstract

Objectives. The problem of choosing the best methods and programs for circuit implementation as part of digital ASIC (Application-Specific Integrated Circuit) sparse systems of disjunctive normal forms (DNF) of completely defined Boolean functions is considered. For matrix forms of sparse DNF systems, the ternary matrix specifying elementary conjunctions contains a large proportion of undefined values corresponding to missing literals of Boolean input variables, and the Boolean matrix specifying the occurrences of conjunctions in DNF functions contains a large proportion of zero values.Methods. It is proposed to investigate various methods of technologically independent logical optimization performed at the first stage of logical synthesis: joint minimization of systems of functions in the DNF class, separate and joint minimization in classes of multilevel representations in the form of Boolean networks and BDD representations using mutually inverse cofactors, as well as the division of a system of functions into subsystems with a limited number of input variables and the method of block cover of DNF systems, focused on minimizing the total area of the blocks forming the cover.Results. When implementing sparse DNF systems of Boolean functions in ASIC, along with traditional methods of joint minimization of systems of functions in the DNF class, methods for optimizing multilevel representations of Boolean function systems based on Shannon expansions can be used for technologically independent optimization, while separate minimization and joint minimization of the entire system as a whole turn out to be less effective compared with block partitions and coatings of the DNF system and subsequent minimization of multilevel representations. Schemes obtained as a result of synthesis using minimized representations of Boolean networks often have a smaller area than schemes obtained using minimized BDD representations.Conclusion. For the design of digital ASIC, the effectiveness of combined approach is shown, when initially the block coverage programs of the DNF system is used, followed by the use of programs to minimize multilevel block representations in the form of Boolean networks minimized based on Shannon expansion.