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.