The search for subsystems of related functions from multilevel representation of systems of Boolean functions1

Abstract

One of the directions of logical optimization of multilevel representations of systems of Boolean functions is the methods based on the search of subsystems of functions that have the same parts in the domains of functions of selected subsystems. Such subsystems are called related. The good relationship of functions leads to the appearance of a large number of identical structural parts (conjunctions, algebraic expressions, subfunctions, etc.) in optimized forms of representation of functions which are used in the construction of combinational logic circuits. The more the functions of the selected subsystem are related, the sooner it is expected that in the representations of the functions of this subsystem will be more identical subexpressions and synthesized logic circuits will have less complexity. We describe software-implemented algorithms for extracting subsystems of related functions from a BDD representation of a system of Boolean functions based on introduced numerical estimates of the relationship of BDD representations of functions. The relationship of Boolean functions is the presence of Boolean vectors, where the functions take the value as one, or of the same equations in BDD representations. BDD representations of Boolean functions are compact forms defining functions and are constructed as the result of Shannon decomposition of the functions of the original system (resulting from the decomposition of subfunctions) by all variables, which the functions of the original system depend on. The experiments show the effectiveness of proposed algorithms and programs in the synthesis of logic circuits from logic elements library.

Keywords

• boolean function
• shannon decomposition
• bdd representation
• disjunctive normal form
• logic synthesis