The Subtrace Order and Counting First-Order Logic

Abstract

We study the subtrace relation among Mazurkiewicz traces which generalizes the much-studied subword order. Here, we consider the 2-variable fragment of a counting extension of first-order logic with regular predicates. It is shown that all definable trace languages are effectively recognizable implying that validity of a sentence of this logic is decidable (this problem is known to be undecidable for virtually all stronger logics already for the subword relation).