Copyless cost-register automata: Structure, expressiveness, and closure properties

Abstract

Cost register automata (CRA) and its subclass, copyless CRA, were recently proposed by Alur et al. as a new model for computing functions over strings. We study some structural properties, expressiveness, and closure properties of copyless CRA. We show that copyless CRA are strictly less expressive than weighted automata and are not closed under reverse operation. To find a better class we impose restrictions on copyless CRA, which ends successfully with a new robust computational model that is closed under reverse and other extensions.

On Polynomial Recursive Sequences

“…To avoid technical details, we simply observe that CRAs over unary alphabets recognize exactly poly-recursive sequences, as defined in Definition 2.1. Since [4,7,21] discuss several variants of CRAs, to avoid ambiguity we refer to the definition of a CRA that can be found in [19]. 2 Weighted Context-Free Grammars (WCFG) Weighted automata can be equivalently defined as an extension of finite automata, where each translation is labelled by an element of the semiring S (see e.g.…”

Weak Cost Register Automata Are Still Powerful

“…Indeed, no register is used twice in any update function; this property is called copylessness. This syntactic restriction, introduced by Alur et al [2] and studied by Mazowiecki and Riveros [6], provably weakens the model. It was the hope of Alur et al that this would provide a model for which equivalence is decidable.…”

Pumping lemmas for weighted automata

“…The class of functions computed by WA enjoys several equivalent representations in terms of automata and logics. Alur et al introduced the model of cost register automata (CRA for short) [ADD + 13, AR13], an alternative model to compute functions over words inspired by programming paradigms, that recently received a lot of attention [MR,MR19, min-plus and max-plus semirings. More recently, [DG19] studied aperiodic WA over arbitrary weights, relating fragments of aperiodic WA with various degrees of ambiguity, and providing separating examples over the min-plus, max-plus and the natural semiring.…”

“…However, to our knowledge, there is no reference for a strict inclusion between polynomially-ambiguous automata and the full class of WA. There is some work on the semiring of rational numbers with the usual sum and product [MR19,BFLM20]. In these papers the polynomially-ambiguous fragment over the one-letter alphabet is characterised in terms of a fragment of linear recurrence sequences.…”