Towards an algebraic theory of Boolean circuits
Boolean circuits are used to represent programs on finite data. Reversible Boolean circuits and quantum Boolean circuits have been introduced to modelize some physical aspects of computation. Those notions are essential in complexity theory, but we claim that a deep mathematical theory is needed to...
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| Published in | Journal of pure and applied algebra Vol. 184; no. 2; pp. 257 - 310 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier B.V
01.11.2003
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| Subjects | |
| Online Access | Get full text |
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| Summary: | Boolean circuits are used to represent programs on finite data.
Reversible Boolean circuits and
quantum Boolean circuits have been introduced to modelize some physical aspects of computation. Those notions are essential in complexity theory, but we claim that a deep mathematical theory is needed to make progress in this area. For that purpose, the recent developments of
knot theory is a major source of inspiration.
Following the ideas of Burroni, we consider logical gates as
generators for some algebraic structure with two compositions, and we are interested in the
relations satisfied by those generators. For that purpose, we introduce
canonical forms and
rewriting systems. Up to now, we have mainly studied the
basic case and the
linear case, but we hope that our methods can be used to get presentations by generators and relations for the (reversible)
classical case and for the (unitary)
quantum case. |
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| ISSN: | 0022-4049 1873-1376 |
| DOI: | 10.1016/S0022-4049(03)00069-0 |