Slender Siromoney matrix languages

A Siromoney matrix grammar is a simple device for the generation of rectangular pictures. In this paper we discuss Siromoney matrix grammars whose picture language are slender, i.e., they contain only a bounded number of pictures for each size. In particular, it is shown that the slenderness decision problem is decidable for Siromoney matrix grammars with context-free rules. Moreover, some closure and decidability questions for slender Siromoney matrix languages are discussed.