The Boolean Closure of Growing Context-Sensitive Languages

Article type: Research Article

Authors: Jurdziński, Tomasz

Affiliations: Institute of Computer Science, University of Wrocław, Joliot-Curie 15, PL-50-383 Wrocław, Poland. tju@ii.uni.wroc.pl

Note: [] Address for correspondence: Institute of Computer Science, University of Wrocław, Joliot-Curie 15, PL-50-383 Wrocław, Poland

Abstract: The set of growing context-sensitive languages (GCSL) is a naturally defined subclass of context-sensitive languages whose membership problem is solvable in polynomial time. Moreover, growing context-sensitive languages and their deterministic counterpart called Church-Rosser Languages (CRL) complement the Chomsky hierarchy in a natural way [13]. In this paper, closures of GCSL under the boolean operations are investigated. It is shown that there exists an infinite intersection hierarchy for GCSL and CRL, answering an open problem from [2]. Furthermore, the expressive power of the boolean closures of GCSL, CRL, CFL and LOGCFL are compared.

Journal: Fundamenta Informaticae, vol. 89, no. 2-3, pp. 289-305, 2008