2012/10/03 by Wolfram Bentz, Bentz, Wolfram, Brian A. Davey +6
Computer Science · Decision Sciences · Mathematics · #Advanced Algebra and Logic #FOS: Mathematics #Fuzzy and Soft Set Theory #Rings and Algebras (math.RA) #math.RA #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1210.1475
arxiv created 2012/10/03 · openalex publication_date 2012/10/03 · arxiv updated 2012/10/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We make a start on one of George McNulty's Dozen Easy Problems: "Which finite automatic algebras are dualizable?" We give some necessary and some sufficient conditions for dualizability. For example, we prove that a finite automatic algebra is dualizable if its letters act as an abelian group of permutations on its states. To illustrate the potential difficulty of the general problem, we exhibit an infinite ascending chain \mathbf A1 ≤ \mathbf A2 ≤ \mathbf A3 ≤ ...b of finite automatic algebras that are alternately dualizable and non-dualizable.