2016/09/25 by Samuel J. van Gool, Samuel J. v. Gool, Gool, Samuel J. v. +2
Computer Science · Mathematics · #03C50 #03D05 #20M35 #68Q45 #Algebra over a field #Aperiodic graph #Artificial intelligence #Class (philosophy) #Combinatorics #Computability, Logic, AI Algorithms #Computer science #Discrete mathematics #Duality (order theory) #Equivalence (formal languages) #F.4.3 #FOS: Computer and information sciences #FOS: Mathematics #Formal Languages and Automata Theory (cs.FL) #Geometric and Algebraic Topology #Geometry #Group Theory (math.GR) #Logic (math.LO) #Mathematical proof #Mathematics #Monoid #Pure mathematics #Rings and Algebras (math.RA) #Word (group theory) #acm:03C50 #acm:03D05 #acm:20M35 #acm:68Q45 #cs.FL #math.GR #math.LO #math.RA #msc:03C50 #msc:03D05 #msc:20M35 #msc:68Q45 #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1609.07736
Technical report, submitted
openalex publication_date 2016/09/25 · openalex created_date 2016/10/07 · arxiv created 2017/08/28 · arxiv updated 2017/08/30 · openalex updated_date 2026/08/06
We apply Stone duality and model theory to study the structure theory of free pro-aperiodic monoids. Stone duality implies that elements of the free pro-aperiodic monoid may be viewed as elementary equivalence classes of pseudofinite words. Model theory provides us with saturated words in each such class, i.e., words in which all possible factorizations are realized. We give several applications of this new approach, including a solution to the word problem for ω-terms that avoids using McCammond's normal forms, as well as new proofs and extensions of other structural results concerning free pro-aperiodic monoids.