A Classical Propositional Logic for Reasoning About Reversible Logic Circuits

  • Holger Bock Axelsen
  • Robert Glück
  • Robin Kaarsgaard
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9803)


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 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 verification of both reversible circuits and template-based reversible circuit rewriting systems.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Holger Bock Axelsen
    • 1
  • Robert Glück
    • 1
  • Robin Kaarsgaard
    • 1
  1. 1.DIKU, Department of Computer ScienceUniversity of CopenhagenCopenhagenDenmark

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