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Learning correction grammars
 Proceedings of the 20th Annual Conference on Learning Theory, 2007. To appear. 10 For u > 1, u; b 2 N, the
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All intext references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately.
Dynamically Delayed Postdictive Completeness and Consistency in Learning
, 2008
"... In computational function learning in the limit, an algorithmic learner tries to find a program for a computable function g given successively more values of g, each time outputting a conjectured program for g. A learner is called postdictively complete iff all available data is correctly postdicted ..."
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In computational function learning in the limit, an algorithmic learner tries to find a program for a computable function g given successively more values of g, each time outputting a conjectured program for g. A learner is called postdictively complete iff all available data is correctly postdicted by each conjecture. Akama and Zeugmann presented, for each choice of natural number δ, a relaxation to postdictive completeness: each conjecture is required to postdict only all except the last δ seen data points. This paper extends this notion of delayed postdictive completeness from constant delays to dynamically computed delays. On the one hand, the delays can be different for different data points. On the other hand, delays no longer need to be by a fixed finite number, but any type of computable countdown is allowed, including, for example, countdown in a system of ordinal notations and in other graphs disallowing computable infinitely descending counts. We extend many of the theorems of Akama and Zeugmann and provide some feasible learnability results. Regarding fairness in feasible learning, one needs to limit use of tricks that postpone output hypotheses until there is enough time to think about them. We see, for polytime learning, postdictive completeness (and delayed variants): 1. allows some but not all postponement tricks, and 2. there is a surprisingly tight boundary, for polytime learning, between what postponement is allowed and what is not. For example: 1. the set of polytime computable functions is polytime postdictively completely learnable employing some postponement, but 2. the set of exptime computable functions, while polytime learnable with a little more postponement, is not polytime postdictively completely learnable! We have that, for w a notation for ω, the set of exptime functions is polytime learnable with wdelayed postdictive completeness. Also provided are generalizations to further, small constructive limit ordinals. 1
Directions for Computability Theory Beyond Pure Mathematical
"... This paper begins by briefly indicating the principal, nonstandard motivations of the author for his decades of work in Computability Theory (CT), a.k.a. Recursive Function Theory. Then it discusses its proposed, general directions beyond those from pure mathematics for CT. These directions are as ..."
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This paper begins by briefly indicating the principal, nonstandard motivations of the author for his decades of work in Computability Theory (CT), a.k.a. Recursive Function Theory. Then it discusses its proposed, general directions beyond those from pure mathematics for CT. These directions are as follows. 1. Apply CT to basic sciences, for example, biology, psychology, physics, chemistry, and economics. 2. Apply the resultant insights from 1 to philosophy and, more generally, apply CT to areas of philosophy in addition to the philosophy and foundations of mathematics. 3. Apply CT for insights into engineering and other professional fields. Lastly, this paper provides a progress report on the above nonpure mathematical directions for CT, including examples for biology, cognitive science and learning theory, philosophy of science, physics, applied machine learning, and computational complexity. Interweaved with the report are occasional remarks about the future. 1 Motivations