Title :
Reversible Function Synthesis of Large Reversible Functions with No Ancillary Bits Using Covering Set Partitions
Author :
Hawash, Maher ; Perkowski, Marek ; Bleiler, Steve ; Caughman, John ; Hawash, Amjad
Author_Institution :
Electr. & Comput. Eng., Portland State Univ., Portland, OR, USA
Abstract :
This paper presents a synthesis algorithm, Covering Set Partitions (CSP), for reversible binary functions with no ancillary (garbage) bits. Existing algorithms are constrained to functions of small number of variables because they store the entire truth table of 2n terms in memory or require a huge amount of time to yield results because they must calculate all possible permutations of an input vector. In contrast, the CSP algorithm harnesses the natural mathematical properties of binary numbers, partially ordered sets and covering graph theory, to construct input vectors which are guaranteed to produce valid results. A randomly selected subset of all valid input vectors are processed where the best input vector sequence wins. The CSP algorithm is capable of synthesizing functions of large number of variables (30 bits) in a reasonable amount of time.
Keywords :
digital arithmetic; graph theory; logic design; set theory; vectors; CSP algorithm; ancillary bits; binary numbers; covering graph theory; covering set partition; mathematical properties; partially ordered sets; randomly selected subset; reversible binary function synthesis algorithm; truth table; vector sequence; Algorithm design and analysis; Convergence; Equations; Inverters; Logic gates; Mathematical model; Partitioning algorithms; Covering set partition (CSP); Hasse; MMD; covering graphs; partially ordered sets; reversible;
Conference_Titel :
Information Technology: New Generations (ITNG), 2011 Eighth International Conference on
Conference_Location :
Las Vegas, NV
Print_ISBN :
978-1-61284-427-5
Electronic_ISBN :
978-0-7695-4367-3
DOI :
10.1109/ITNG.2011.174