Fairness in context Free grammars under canonical derivations
In [PFMZ 82] the notion of Fair derivations in context free grammars was introduced and studied. The main result there is a characterization of fairly terminating grammars as non-variable-doubling. In this paper we show that the same characterization is valid under canonical derivations in which the next variable to be expanded is deterministically chosen, leaving nondeterminism only to the decision as to which rule to apply. Two families of canonical derivations are introduced and studied: 1) Spinal derivations and 2) Layered derivations.
KeywordsContext Free Grammar Full Cycle Derivation Tree Sentential Form Infinite Path
Unable to display preview. Download preview PDF.
- [H 84]D. Harel: "A general result about infinite trees and its applications", proc. 16th ACM-STOC, Washington D.C., May 1984.Google Scholar
- [HU 79]J.E. Hopcroft, J.D. Ulmann: "Introduction to automata theory, languages and computation", Addison-Wesley, Reading.Mass., 1979.Google Scholar
- [PFMZ 82]S. Porat, N. Francez, S. Moran, S. Zaks: "Fair derivations in context free grammars", Information and Control 55: 108–116, 1982.Google Scholar
- [RA 84]K.Rangarajan, S.Arun-kumar: "Fair derivations in EOL systems", submited for publication, 1984.Google Scholar