Treating terminals as function values of time

Motivated by the idea of describing parquet deformations using grammars, we define in this paper a terminal weighted grammar where the terminal generated at any step of a derivation is defined as a function of time. It is seen that terminal weighted regular grammars generate exactly the class of recursively enumerable sets. Terminal weighted matrix grammars are used to describe parquet deformations. The hierarchy of families generated by putting various restrictions on the functions is studied.