The class of growing context-sensitive languages (GCSL) is a naturally defined subclass of context-sensitive languages whose membership problem is solvable in polynomial time. GCSL and its deterministic counterpart called Church-Rosser Languages (CRL) complement the Chomsky hierarchy in a natural way [9]. In this paper, the extension of GCSL obtained by closures of this class under the boolean operations are investigated. We show that there exists an infinite intersection hierarchy, answering an open problem from [1]. Further, we compare the expressive power of the boolean closures of GCSL, CRL, CFL and LOGCFL.
['Tomasz Jurdzinski']
The boolean closure of growing context-sensitive languages