State complexity of SBTA languages

Abstract

It has already been established that Systolic Binary Tree Automata (SBTA in short) provide an interesting and robust model for one-way computation on binary-tree networks of memory-less processors and that the corresponding family of languages has nice properties reminding those of regular languages and is their proper superfamily. In this paper we prolong the study of this family of languages by investigating various problems related to their descriptional complexity with respect to the number of states of minimal (deterministic or nodeterministic and stable or ordinary) SBTA: we show the existence of four infinite hierarchies without gaps; we present tight upper bounds on succinctness of description of these languages by SBTA of varius types and we provide tight upper bounds on the state complexity of basic language operations. Such tight bounds seems to have been previously established only for basic operations on regular languages with respect to the number of states of minimal DFA. In order to prove lower bounds we establish in addition several criteria for minimal number of states of a SBTA accepting a SBTA-language as well as a nonacceptability criterion for SBTA-languages.