Complexity classifications for different equivalence and audit problems for Boolean circuits
Elmar B\~A{\P}hler (Universit\"at W\"urzburg), Nadia Creignou, (Universit\'e de la M\'editerran\'ee, Marseille), Matthias Galota, (Elektrobit), Steffen Reith (Hochschule RheinMain, Wiesbaden), Henning, Schnoor (Christian-Albrechts-Universit\"at zu Kiel), Heribert Vollmer
TL;DR
This paper investigates the computational complexity of various equivalence, audit, and enumeration problems for Boolean circuits, identifying cases with efficient algorithms and proving NP-hardness for others.
Contribution
It provides a comprehensive complexity classification for these problems across different gate set restrictions in Boolean circuits.
Findings
Efficient algorithms exist for certain restricted gate sets.
Most other gate types lead to NP-hard problems.
Complexity classifications guide practical circuit analysis.
Abstract
We study Boolean circuits as a representation of Boolean functions and consider different equivalence, audit, and enumeration problems. For a number of restricted sets of gate types (bases) we obtain efficient algorithms, while for all other gate types we show these problems are at least NP-hard.
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