Functionals Using Bounded Information and the Dynamics of Algorithms

We consider computable functionals mapping the Baire space into the set of integers. By continuity, the value of the functional on a given function depends only on a "critical" finite part of this function. Care: there is in general no way to compute this critical finite part without query...

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Veröffentlicht in:2012 27th Annual IEEE Symposium on Logic in Computer Science S. 345 - 354
Hauptverfasser: Grigorieff, S., Valarcher, P.
Format: Tagungsbericht
Sprache:Englisch
Veröffentlicht: IEEE 01.06.2012
Schlagworte:
Abstract state machines
Abstracts
Algorithm design and analysis
Computational modeling
Computer science
Heuristic algorithms
Operational semantics
Semantics
Theory of Algorithms
Topology
Type 2 computability
ISBN:1467322636, 9781467322638
ISSN:1043-6871
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Beschreibung
Zusammenfassung:We consider computable functionals mapping the Baire space into the set of integers. By continuity, the value of the functional on a given function depends only on a "critical" finite part of this function. Care: there is in general no way to compute this critical finite part without querying the function on an arbitrarily larger finite part! Nevertheless, things are different in case there is a uniform bound on the size of the domain of this critical finite part. We prove that, modulo a quadratic blow-up of the bound, one can compute the value of the functional by an algorithm which queries the input function on a uniformly bounded finite part. Up to a constant factor, this quadratic blow-up is optimal. We also characterize such functionals in topological terms using uniformities. As an application of these results, we get a topological characterization of the dynamics of algorithms as modeled by Gurevich's Abstract State Machines.
ISBN:1467322636
9781467322638
ISSN:1043-6871
DOI:10.1109/LICS.2012.45