Exact combinational logic synthesis and non-standard circuit design

Using a new exact synthesizer that automatically induces minimal universal boolean function libraries, we introduce two indicators for comparing their expressiveness: the first based on how many gates are used to synthesize all binary operators, the second based on how many N-variable truth table values are covered by combining up to M gates from the library. By applying the indicators to an exhaustive enumeration of minimal universal libraries, two dual asymmetrical operations, Logic Implication "" and Half XOR "<" are found to consistently outperform their symmetrical counterparts, NAND and NOR. Our expressiveness metrics bring support to the conjecture that asymmetrical operators are significantly more expressive that their well studied symmetric counterparts, omnipresent in various circuit design tools. ACM Categories and Subject Descriptors: B.6 [Logic Design]: B.6.1 [Design Styles]: Combinational logic General Terms: Algorithms, Design, Theory, Measurement...

• Type: Conference
• Year: 2008
• Where: CF
• Authors: Paul Tarau, Brenda Luderman
• Keywords: Applied Computing, CF 2008, Dual Asymmetrical Operations, Minimal Universal Libraries, Universal Boolean Function