2022/11/07 by Jaroslav Nešetřil, Nesetril, J., Patrice Ossona de Mendez +3
Computer Science · #Combinatorics (math.CO) #Computability, Logic, AI Algorithms #FOS: Computer and information sciences #FOS: Mathematics #Formal Methods in Verification #Logic in Computer Science (cs.LO) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2211.03704
openalex publication_date 2022/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that, on bounded expansion classes, every first-order formula with modulo counting is equivalent, in a linear-time computable monadic expansion, to an existential first-order formula. As a consequence, we derive, on bounded expansion classes, that first-order transductions with modulo counting have the same encoding power as existential first-order transductions. Also, modulo-counting first-order model checking and computation of the size of sets definable in modulo-counting first-order logic can be achieved in linear time on bounded expansion classes. As an application, we prove that a class has structurally bounded expansion if and only if it is a class of bounded depth vertex-minors of graphs in a bounded expansion class. We also show how our results can be used to implement fast matrix calculus on bounded expansion matrices over a finite field.