TWO CHARACTERISTIZATIONS OF THE CONTEXT-SENSITIVE LANGUAGES,
Abstract
An n-dimensional bug-automation is a generalization of a finite state acceptor to n-dimensions. With each bug B, is associated the language L(B) which is the set of top rows of n-dimensional rectangular arrays accepted by B. One-dimensional bugs define trivially the regular sets. Two-dimensional bugs define precisely the context-sensitive languages, while bugs of dimension 3 or greater define all the recursively enumerable sets. Finite state acceptors with n two-way non-writing input tapes are also considered. For each such machine M, let domain (M) be the set of all strings which are the first component of some n-tuple of tapes accepted by M. For any n > or = 1, the domains of n-tape finite state acceptors are precisely the same as the languages definable by n-dimensional bugs, so as a corollary, the domains of two-tape two-way finite state acceptors are precisely the contest-sensitive languages. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1969
- Accession Number
- AD0697040
Entities
People
- Michael J. Fischer
Organizations
- Carnegie Mellon University