Mappings of languages by two-tape devices

Abstract

Several devices with two input lines and one output line are introduced. These devices are viewed as transformations which operate on pairs of (ALGOL-like) languages. Among the results proved are the following: (i) a pair consisting of a language and a regular set is transformed into a language; (ii) let ( V, W ) be a pair consisting of a language and a regular set. Then the set of those words w 1 , for which there exists a word w 2 in V so that ( w 1 , w 2 ) is mapped into W , is a language.