A Two-Dimensional Hierarchy for Parallel Rewriting Systems (1994)
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@TECHREPORT{Rambow94atwo-dimensional,
author = {Owen Rambow and Giorgio Satta},
title = {A Two-Dimensional Hierarchy for Parallel Rewriting Systems},
institution = {},
year = {1994}
}
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Abstract
The class of parallel rewriting systems is considered in this work, and the interaction between two complexity measures, that in the literature have been called synchronous parallelism and independent parallelism, is investigated. It is shown that, when the degree of synchronous parallelism is bounded by some constant greater than one, the degree of independent parallelism induces an infinite non-collapsing hierarchy within the family of generated languages. The result is obtained using an original characterization of parallel rewriting systems. Our result combines with other well known properties of synchronous parallelism to reveal the existence of a two-dimensional hierarchy for the family of languages generated by so called finite copying parallel We are grateful to Joost Engelfriet and Ryuichi Nakanisi for helpful discussion on topics related to this paper. This research was conducted while the second author was a post-doctoral fellow at the Institute for Research in Cognitive ...
