Geodesic
An approximate algorithm for computing the complexity of reversible functions in the basis of Toffoli
The Bulletin of Irkutsk State University. Series Mathematics, Tome 4 (2011) no. 4, pp. 12-26

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We investigate questions of computing of the complexity of the arbitrarily given reversible function. Previously introduced the concept of reversible computation required, in particular, the concept of a reversible function. We consider various representations of reversible functions (the table of values, permutation matrices, permutations and logic circuits). As the basis of reversible circuits is considered a well-known Toffoli gates [1]. Presented sequential and parallel algorithms for computing of the complexity of the reversible function. The algorithms were run on a cluster containing 16 nodes, each of which has a Intel Pentium Dual CPU, 1,86 Gz, 1,87 Gz, 2Gb, Ethernet network 100Mbit/sek. The cluster is organized in ESSAE. We present estimates of the complexity.
Keywords: reversible functions, complexity, Toffoli gates, sequential and parallel algorithms. 
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S. F. Vinokurov; A. S. Frantseva. An approximate algorithm for computing the complexity of reversible functions in the basis of Toffoli. The Bulletin of Irkutsk State University. Series Mathematics, Tome 4 (2011) no. 4, pp. 12-26. http://geodesic.mathdoc.fr/item/IIGUM_2011_4_4_a1/