On the Learnability of Monotone Functions
نویسنده
چکیده
On the Learnability of Monotone Functions
منابع مشابه
Evolvability need not imply learnability
We show that Boolean functions expressible as monotone disjunctive normal forms are PAC-evolvable under a uniform distribution on the Boolean cube if the hypothesis size is allowed to remain fixed. We further show that this result is insufficient to prove the PAC-learnability of monotone Boolean functions, thereby demonstrating a counter-example to a recent claim to the contrary. We further dis...
متن کاملLearnability of Some Eecient Representations of Boolean Functions
This thesis studies the learnability of several representation classes of Boolean functions: a restriction on k-term DNF, ordered binary decision diagrams and monotone term decision lists. We also show that some operations on these representation classes can be done in polynomial time. This fact is one of the motivations of the study (and use) of those classes.
متن کاملGENERALIZED POSITIVE DEFINITE FUNCTIONS AND COMPLETELY MONOTONE FUNCTIONS ON FOUNDATION SEMIGROUPS
A general notion of completely monotone functionals on an ordered Banach algebra B into a proper H*-algebra A with an integral representation for such functionals is given. As an application of this result we have obtained a characterization for the generalized completely continuous monotone functions on weighted foundation semigroups. A generalized version of Bochner’s theorem on foundation se...
متن کاملLearning Circuits with few Negations
Monotone Boolean functions, and the monotone Boolean circuits that compute them, have been intensively studied in complexity theory. In this paper we study the structure of Boolean functions in terms of the minimum number of negations in any circuit computing them, a complexity measure that interpolates between monotone functions and the class of all functions. We study this generalization of m...
متن کاملOptimal Cryptographic Hardness of Learning Monotone Functions
A wide range of positive and negative results have been established for learning different classes of Boolean functions from uniformly distributed random examples. However, polynomial-time algorithms have thus far been obtained almost exclusively for various classes of monotone functions, while the computational hardness results obtained to date have all been for various classes of general (non...
متن کامل