Search results for "recursive"

Co-learning of total recursive functions

1994

Co-learnability and FIN-identifiability of enumerable classes of total recursive functions

1994

Co-learnability is an inference process where instead of producing the final result, the strategy produces all the natural numbers but one, and the omitted number is an encoding of the correct result. It has been proved in [1] that co-learnability of Goedel numbers is equivalent to EX-identifiability. We consider co-learnability of indices in recursively enumerable (r.e.) numberings. The power of co-learnability depends on the numberings used. Every r.e. class of total recursive functions is co-learnable in some r.e. numbering. FIN-identifiable classes are co-learnable in all r.e. numberings, and classes containing a function being accumulation point are not co-learnable in some r.e. number…

Unions of identifiable classes of total recursive functions

1992

J.Barzdin [Bar74] has proved that there are classes of total recursive functions which are EX-identifiable but their union is not. We prove that there are no 3 classes U1, U2, U3 such that U1∪U2,U1∪U3 and U2∪U3 would be in EX but U1∪U2∪U3∉ EX. For FIN-identification there are 3 classes with the above-mentioned property and there are no 4 classes U1, U2, U3, U4 such that all 4 unions of triples of these classes would be identifiable but the union of all 4 classes would not. For identification with no more than p minchanges a (2p+2−1)-tuple of such classes do exist but there is no (2p+2)-tuple with the above-mentioned properly.

Structured Frequency Algorithms

2015

B.A. Trakhtenbrot proved that in frequency computability (introduced by G. Rose) it is crucially important whether the frequency exceeds \(\frac{1}{2}\). If it does then only recursive sets are frequency-computable. If the frequency does not exceed \(\frac{1}{2}\) then a continuum of sets is frequency-computable. Similar results for finite automata were proved by E.B. Kinber and H. Austinat et al. We generalize the notion of frequency computability demanding a specific structure for the correct answers. We show that if this structure is described in terms of finite projective planes then even a frequency \(O(\frac{\sqrt{n}}{n})\) ensures recursivity of the computable set. We also show that …

On the inductive inference of recursive real-valued functions

1999

AbstractWe combine traditional studies of inductive inference and classical continuous mathematics to produce a study of learning real-valued functions. We consider two possible ways to model the learning by example of functions with domain and range the real numbers. The first approach considers functions as represented by computable analytic functions. The second considers arbitrary computable functions of recursive real numbers. In each case we find natural examples of learnable classes of functions and unlearnable classes of functions.

Memory limited inductive inference machines

1992

The traditional model of learning in the limit is restricted so as to allow the learning machines only a fixed, finite amount of memory to store input and other data. A class of recursive functions is presented that cannot be learned deterministically by any such machine, but can be learned by a memory limited probabilistic leaning machine with probability 1.

Learning by the Process of Elimination

2002

AbstractElimination of potential hypotheses is a fundamental component of many learning processes. In order to understand the nature of elimination, herein we study the following model of learning recursive functions from examples. On any target function, the learning machine has to eliminate all, save one, possible hypotheses such that the missing one correctly describes the target function. It turns out that this type of learning by the process of elimination (elm-learning, for short) can be stronger, weaker or of the same power as usual Gold style learning.While for usual learning any r.e. class of recursive functions can be learned in all of its numberings, this is no longer true for el…

On the duality between mechanistic learners and what it is they learn

1993

All previous work in inductive inference and theoretical machine learning has taken the perspective of looking for a learning algorithm that successfully learns a collection of functions. In this work, we consider the perspective of starting with a set of functions, and considering the collection of learning algorithms that are successful at learning the given functions. Some strong dualities are revealed.

Transformations that preserve learnability

1996

We consider transformations (performed by general recursive operators) mapping recursive functions into recursive functions. These transformations can be considered as mapping sets of recursive functions into sets of recursive functions. A transformation is said to be preserving the identification type I, if the transformation always maps I-identifiable sets into I-identifiable sets.

Ridge-line optimal detector

2000

Image processing techniques have seen many developments in recent years. Starting from the pioneering work of Canny, Deriche developed a second order recursive filter capable of detecting stepped contours. However, there are other contour shapes that those filters struggle to detect. We describe a new optimal filter sensu Canny for detecting ridge-line contours. This is a third order recursive and even filter. It is dependent on three parameters by which detection accuracy is adjusted. The results obtained by applying this filter to (possibly noise- affected) images are compared with those in the work by Ziou. © 2000 Society of Photo-Optical Instrumentation Engineers. (S0091-3286(00)00706-6)