Term rewriting and all that
Transformation rules for designing CNOT-based quantum circuits
Proceedings of the 39th annual Design Automation Conference
Proceedings of the 7th Colloquium on Automata, Languages and Programming
A transformation based algorithm for reversible logic synthesis
Proceedings of the 40th annual Design Automation Conference
Fredkin/Toffoli Templates for Reversible Logic Synthesis
Proceedings of the 2003 IEEE/ACM international conference on Computer-aided design
Principles of a reversible programming language
Proceedings of the 5th conference on Computing frontiers
Irreversibility and heat generation in the computing process
IBM Journal of Research and Development
Rule-based optimization of reversible circuits
Proceedings of the 2010 Asia and South Pacific Design Automation Conference
Describing and optimising reversible logic using a functional language
IFL'11 Proceedings of the 23rd international conference on Implementation and Application of Functional Languages
Exact Template Matching Using Boolean Satisfiability
ISMVL '13 Proceedings of the 2013 IEEE 43rd International Symposium on Multiple-Valued Logic
Upper bounds for reversible circuits based on Young subgroups
Information Processing Letters
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The increased effort in recent years towards methods for computer aided design of reversible logic circuits has also lead to research in algorithms for optimising the resulting circuits; both with higher-level data structures and directly on the reversible circuits. To obtain structural patterns that can be replaced by a cheaper realisation, many direct algorithms apply so-called moving rules; a simple form of rewrite rules that can only swap gate order. In this paper we first describe the few basic rules that are needed to perform rewriting directly on reversible logic circuits made from general Toffoli circuits. We also show how to use these rules to derive more complex formulas. The major difference compared to existing approaches is the use of negative controls (white dots), which significantly increases the algebraic strength. We show how existing optimisation approaches can be adapted as problems based on our rewrite rules. Finally, we outline a path to generalising the rewrite rules by showing their forms for reversible control-gates. This can be used to expand our method to other gates such as the controlled-swap gate or quantum gates.