An infinite hierarchy induced by depth synchronization

Authors:
Franziska Biegler;Ian McQuillan;Kai Salomaa
Affiliations:
Department of Computer Science, University of Western Ontario, London, ON, N6A 5B7, Canada;Department of Computer Science, University of Saskatchewan, Saskatoon, SK S7N 5A9, Canada;School of Computing, Queens University, Kingston, ON K7L 3N6, Canada
Venue:
Theoretical Computer Science
Year:
2007

Citing 9
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On the synchronized derivation depth of context-free grammars

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Abstract

Depth-synchronization measures the number of parallel derivation steps in a synchronized context-free (SCF) grammar. When not bounded by a constant the depth-synchronization measure of an SCF grammar is at least logarithmic and at most linear with respect to the word length. Languages with linear depth-synchronization measure and languages with a depth-synchronization measure in between logarithmic and linear are proven to exist. This gives rise to a strict infinite hierarchy within the family of SCF (and ET0L) languages.