Mappings which Preserve Context Sensitive Languages

A basic result which gives a condition under which a (possibly length-decreasing) homomorphism preserves a contest. sensitive language is presented. Using this result, conditions under which pushdown transducers and linear bounded transducers preserve contest sensitive languages are given. The basic result is also applied to show that certain rewriting systems generate context sensitive languages instead of arbitrary recursively enumerable sets. Of special interest is the result that if each rule in a rewriting system has a terminal letter on its right side, then the language generated is context free.