The Delta Operation: From Strings to Trees to Strings

Abstract

The delta of a language L consists of the yields of trees of which all paths are in L. The context-free languages are the deltas of the regular languages. The indexed languages are the deltas of the deterministic context-free languages. In general, the nondeterministic (n+1)-iterated pushdown languages are the deltas of the deterministic n- iterated pushdown languages. The recursively enumerable languages are the deltas of the context-free languages. The delta of a string relation R consists of the yields of trees of which all paths are in the R-image of one string. The ET0L languages are the deltas of the relations recognized by deterministic two-tape finite automata. The recursively enumerable languages are the deltas of the finite state transductions.