Automaton analogs of syntax directed translation schemata

This paper is a compendium of recent results obtained in the area of syntax directed translations. It is shown that there exists an infinite hierarchy of syntax directed translations in terms of the number of variables allowed on the right side of productions of the underlying context free grammar. An automaton for the formal specification of translations, called a pushdown assembler, is introduced. A k-register pushdown assembler is a pushdown automaton which has k passive registers associated with each level on the pushdown tape. Each register can hold a string of output symbols, and when a level is erased, the contents of the registers are concatenated together and passed to the level below. Two types of pushdown assembler are considered. One model, called the type A pushdown assembler or A-machine, can write output strings into empty registers at the top level only. The other model, the B-machine, can concatenate arbitrarily many output strings to the left or right of the present contents of a register at the top level. The A-machines provide an exact characterization for the syntax directed translations. The B-machines define a new larger class of translations having many properties possessed by the syntax directed translations. In addition, we show that a B-machine with one register per level is equivalent to an A-machine with two registers per level.