Logical optimization the multilevel representations of systems of Boolean functions based on partitioning into blocksand Shannon decomposition

Abstract

The results of experimental study of the effectiveness of optimization procedures for systems of Boolean functions which are used in the synthesis of combinational circuits are described. The procedures use algorithms for partitioning systems of functions into subsystems and algorithms for optimizing multilevel representations of functions based on Shannon decomposition. The Shannon decomposition uses the procedure for finding inverse subfunctions, contained in decomposition result (BDDI-optimization). It is shown that these procedures can reduce the area of combinational circuits from library gates in many cases in the process of synthesis. Joint BDDI optimization is more preferable method in comparison to separate technologically independent BDDI optimization, since the area of circuits built on joint BDDI is smaller than the area of circuits built on separate BDDI in most cases.

Keywords

• boolean function
• disjunctive normal form
• binary decision diagram (bdd)
• partitioning systems of functions
• synthesis of logical circuit
• cmos-technology