Search results for "Numbering"
showing 7 items of 7 documents
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…
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…
Kolmogorov numberings and minimal identification
1995
Identification of programs for computable functions from their graphs by algorithmic devices is a well studied problem in learning theory. Freivalds and Chen consider identification of ‘minimal’ and ‘nearly minimal’ programs for functions from their graphs. To address certain problems in minimal identification for Godel numberings, Freivalds later considered minimal identification in Kolmogorov Numberings. Kolmogorov numberings are in some sense optimal numberings and have some nice properties. We prove certain hierarchy results for minimal identification in every Kolmogorov numbering. In addition we also compare minimal identification in Godel numbering versus minimal identification in Kol…
Indexing Method for Transitive Relationships of Product Information
2008
To successfully use a relational database management system (RDBMS) as a repository for product information, the RDBMS must efficiently process and properly answer ontological queries. The key to processing the ontological queries is whether the various semantic relationships among the concepts of the product ontology are likewise well-processed. In particular, the transitive relationships (e.g., is-a, component-of relationships) such as ancestors-descendents, parents-children, and taxonomy of products must be processed successfully. We propose an efficient index using a numbering scheme (labeling scheme) to process queries over transitive relationships. (This paper is an extended version o…
Proposal for generalised supersymmetry Les Houches Accord for see-saw models and PDG numbering scheme
2013
The SUSY Les Houches Accord (SLHA) 2 extended the first SLHA to include various generalisations of the Minimal Supersymmetric Standard Model (MSSM) as well as its simplest next-to-minimal version. Here, we propose further extensions to it, to include the most general and well-established see-saw descriptions (types I/II/III, inverse, and linear) in both an effective and a simple gauged extension of the MSSM framework. In addition, we generalise the PDG numbering scheme to reflect the properties of the particles
Kolmogorov numberings and minimal identification
1997
Abstract Identification of programs for computable functions from their graphs by algorithmic devices is a well studied problem in learning theory. Freivalds and Chen consider identification of ‘minimal’ and ‘nearly minimal’ programs for functions from their graphs. To address certain problems in minimal identification for Godel numberings, Freivalds later considered minimal identification in Kolmogorov numberings. Kolmogorov numberings are in some sense optimal numberings and have some nice properties. We prove certain separation results for minimal identification in every Kolmogorov numbering. In addition we also compare minimal identification in Godel numberings versus minimal identifica…
Inductive inference of recursive functions: Complexity bounds
2005
This survey includes principal results on complexity of inductive inference for recursively enumerable classes of total recursive functions. Inductive inference is a process to find an algorithm from sample computations. In the case when the given class of functions is recursively enumerable it is easy to define a natural complexity measure for the inductive inference, namely, the worst-case mindchange number for the first n functions in the given class. Surely, the complexity depends not only on the class, but also on the numbering, i.e. which function is the first, which one is the second, etc. It turns out that, if the result of inference is Goedel number, then complexity of inference ma…