Stability of Boolean function classes with respect to clones of linear functions

DOI10.1007/S11083-022-09596-5arXiv2101.06691MaRDI QIDQ6358453

Erkko Lehtonen, Miguel Couceiro

Publication date: 17 January 2021

Abstract: We consider classes of Boolean functions stable under compositions both from the right and from the left with clones. Motivated by the question how many properties of Boolean functions can be defined by means of linear equations, we focus on stability under compositions with the clone of linear idempotent functions. It follows from a result by Sparks that there are countably many such linearly definable classes of Boolean functions. In this paper, we refine this result by completely describing these classes. This work is tightly related with the theory of function minors, stable classes, clonoids, and hereditary classes, topics that have been widely investigated in recent years by several authors including Maurice Pouzet and his coauthors.

Mathematics Subject Classification ID

Order, lattices, ordered algebraic structures (06-XX)

Related Items (2)

Near-unanimity-closed minions of Boolean functions ⋮ Clonoids between modules

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