A Classical Propositional Logic for Reasoning About Reversible Logic Circuits [chapter]

Holger Bock Axelsen, Robert Glück, Robin Kaarsgaard
2016 Lecture Notes in Computer Science  
We propose a syntactic representation of reversible logic circuits in their entirety, based on Feynman's control interpretation of Toffoli's reversible gate set. A pair of interacting proof calculi for reasoning about these circuits is presented, based on classical propositional logic and monoidal structure, and a natural order-theoretic structure is developed, demonstrated equivalent to Boolean algebras, and extended categorically to form a sound and complete semantics for this system. We show
more » ... that all strong equivalences of reversible logic circuits are provable in the system, derive an equivalent equational theory, and describe its main applications in the verication of both reversible circuits and template-based reversible circuit rewriting systems.
doi:10.1007/978-3-662-52921-8_4 fatcat:ondwguxmpbb3jklvp6irgwatuu