Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
On the Complexity of Mod-2l Sum PLA's
IEEE Transactions on Computers
Efficient Boolean function matching
ICCAD '92 1992 IEEE/ACM international conference proceedings on Computer-aided design
Boolean matching in logic synthesis
EURO-DAC '92 Proceedings of the conference on European design automation
Boolean matching using generalized Reed-Muller forms
DAC '94 Proceedings of the 31st annual Design Automation Conference
Generalized Reed-Muller Forms as a Tool to Detect Symmetries
IEEE Transactions on Computers
ICCD '92 Proceedings of the 1991 IEEE International Conference on Computer Design on VLSI in Computer & Processors
On a New Boolean Function with Applications
IEEE Transactions on Computers
Hypergraph isomorphism and structural equivalence of Boolean functions
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Exact minimization of fixed polarity Reed-Muller expressions for incompletely specified functions
ASP-DAC '00 Proceedings of the 2000 Asia and South Pacific Design Automation Conference
A Comment on "Generalized Reed-Muller Forms as a Tool to Detect Symmetries"
IEEE Transactions on Computers
Efficient computation of canonical form for Boolean matching in large libraries
Proceedings of the 2004 Asia and South Pacific Design Automation Conference
A Comment on "Boolean Functions Classification via Fixed Polarity Reed-Muller Form'
IEEE Transactions on Computers
Extending symmetric variable-pair transitivities using state-space transformations
Proceedings of the great lakes symposium on VLSI
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In this paper, we present a new method to characterize completely specified Boolean functions. The central theme of the classification is the functional equivalence (a.k.a. Boolean matching). Two Boolean functions are equivalent if there exists input permutation, input negation, or output negation that can transform one function to the other. We have derived a method that can efficiently identify equivalence classes of Boolean functions. The well-known canonical Fixed Polarity Reed-Muller (FPRM) forms are used as a powerful analysis tool. The necessary transformations to derive one function from the other are inherent in the FPRM representations. To identify uniquely each equivalence class, a set of well-known characteristics of Boolean functions and their variables (including linearity, symmetry, total symmetry, self-complement, and self-duality) are employed. It is shown that all the equivalence classes of four-variable functions [10] are uniquely identified where majority of the classes have a single FPRM form as their representative. The Boolean matching has applications in technology mapping and in design of standard cell libraries.