On nilpotent languages and their characterization by regular expressions

Abstract

Tree languages recognized by deterministic root-to-frontier recognizers are also called DR-languages. The concept of generalized R-chain languages was introduced by the author in his paper On monotone languages and their characterization by regular expressions (Acta Cybernetica, 18 (2007), 117-134.) and it has turned out that the monotone DR-languages are exactly those languages that can be given by generalized R-chain languages. In this paper we give a similar characterization for nilpotent DR-languages by means of plain R-chain languages. Also a regular expression based characterization is given for nilpotent string languages.