Quantitative Coding and Complexity Theory of Compact Metric Spaces

Specifying a computational problem requires fixing encodings for input and output: encoding graphs as adjacency matrices, characters as integers, integers as bit strings, and vice versa. For such discrete data, the actual encoding is usually straightforward and/or complexity-theoretically inessential (up to polynomial time, say); but concerning continuous data, already real numbers naturally suggest various encodings with very different computational properties. With respect to qualitative computability, Kreitz and Weihrauch (1985) had identified ADMISSIBILITY as crucial property for 'reasonable' encodings over the Cantor space of infinite binary sequences, so-called representations [doi:10.1007/11780342_48]: For (precisely) these does the sometimes so-called MAIN THEOREM apply, characterizing continuity of functions in terms of continuous realizers. We rephrase qualitative admissibility as continuity of both the representation and its multivalued inverse, adopting from [doi:10.4115/jla.2013.5.7] a notion of sequential continuity for multifunctions. This suggests its quantitative refinement as criterion for representations suitable for complexity investigations. Higher-type complexity is captured by replacing Cantor's as ground space with Baire or any other (compact) ULTRAmetric space: a quantitative counterpart to equilogical spaces in computability [doi:10.1016/j.tcs.2003.11.012]

Plasma Dynamics

Contains reports on six research projects.National Science Foundation (Grant ENG79-07047)U.S. Air Force - Office of Scientific Research (Grant AFOSR77-3143D)U.S. Air Force - Office of Scientific Research (Contract AFOSR82-0063)U.S. Department of Energy (Contract DE-ACO2-78-ET-51013)U.S. Department of Energy (Contract DE-AC02-78ET-53073.A002

Plasma Dynamics

Contains reports on ten research projects divided into two sections.National Science Foundation (Grant ENG79-07047)U.S. Air Force - Office of Scientific Research (Grant AFOSR-77-3143)U.S. Department of Energy (Contract DE-ACO2-78ET51013)U.S. Department of Energy (Contract DE-ASO2-78ET53073.AO02)U.S. Department of Energy (Contract ET-78-S-02-4682)U.S. Department of Energy (Contract DE-AS02-78ET53074)U.S. Department of Energy (Contract DE-ASO2-78ET53050)U.S. Department of Energy (Contract DE-AS02-78ET51002)U.S. Department of Energy (Contract DE-ASO2-78ET53076