scholarly journals On the Learnability of Possibilistic Theories

2020 ◽  
Author(s):  
Cosimo Persia ◽  
Ana Ozaki
Keyword(s):  
Large Class ◽  
Polynomial Time ◽  
Classical Logic ◽  
Learning Model ◽  
Membership Queries ◽  
Exact Model ◽  
Exact Learning ◽  
Probably Approximately Correct ◽  
Horn Theories ◽  
Pac Model

We investigate learnability of possibilistic theories from entailments in light of Angluin’s exact learning model. We consider cases in which only membership, only equivalence, and both kinds of queries can be posed by the learner. We then show that, for a large class of problems, polynomial time learnability results for classical logic can be transferred to the respective possibilistic extension. In particular, it follows from our results that the possibilistic extension of propositional Horn theories is exactly learnable in polynomial time. As polynomial time learnability in the exact model is transferable to the classical probably approximately correct (PAC) model extended with membership queries, our work also establishes such results in this model.

ORACLES IN $\Sigma^p_2$ ARE SUFFFICIENT FOR EXACT LEARNING

2000 ◽  
Vol 11 (04) ◽  
pp. 613-632 ◽  
Author(s):  
Johannes Köbler ◽  
Wolfgang Lindner
Keyword(s):  
Polynomial Time ◽  
Learning Model ◽  
Query Complexity ◽  
Boolean Circuits ◽  
Membership Queries ◽  
Exact Learning ◽  
Equivalence Queries

We study the learnability of representation classes in Angluin's exact learning model. In particular, we consider the following three query types: equivalence queries, equivalence and membership queries, and membership queries only. We show in all three cases that polynomial query complexity implies already polynomial-time learnability, provided that the learner additionally has access to an oracle in [Formula: see text]. It follows that boolean circuits are polynomial-time learnable with equivalence queries and the help of an oracle in [Formula: see text].a

LEARNING CLASSES OF LINEARLY SEPARABLE BOOLEAN FUNCTIONS FROM POSITIVE EXAMPLES

1992 ◽  
Vol 03 (01) ◽  
pp. 41-54
Author(s):  
PAOLA CAMPADELLI ◽  
ANNA MORPURGO
Keyword(s):  
Lower Bound ◽  
Sample Size ◽  
Polynomial Time ◽  
Boolean Functions ◽  
Learning Model ◽  
Probably Approximately Correct Learning ◽  
Probably Approximately Correct

This paper deals with learnability from positive examples of subclasses of linearly separable boolean functions in the framework of the probably approximately correct learning model. We prove that classes of functions defined by binary threshold neurons with n inputs and g(n) unknown weights are learnable in polynomial time iff g(n)=O(log n) and give an upper and a lower bound on the sample size.

scholarly journals Inapproximability and Polynomial-Time Approximation Algorithm for UET Tasks on Structured Processor Networks

2011 ◽  
Vol 2011 ◽  
pp. 1-20 ◽  
Author(s):  
M. Bouznif ◽  
R. Giroudeau
Keyword(s):  
Approximation Algorithm ◽  
Large Class ◽  
Bipartite Graph ◽  
Polynomial Time ◽  
Performance Guarantee ◽  
Makespan Minimization ◽  
Time Approximation ◽  
Polynomial Time Approximation Algorithm ◽  
Precedence Graph ◽  
Polynomial Time Approximation

We investigate complexity and approximation results on a processor networks where the communication delay depends on the distance between the processors performing tasks. We then prove that there is no heuristic with a performance guarantee smaller than 4/3 for makespan minimization for precedence graph on a large class of processor networks like hypercube, grid, torus, and so forth, with a fixed diameter . We extend complexity results when the precedence graph is a bipartite graph. We also design an efficient polynomial-time -approximation algorithm for the makespan minimization on processor networks with diameter .

scholarly journals Actively Learning Concepts and Conjunctive Queries under ELr-Ontologies

2021 ◽  
Author(s):  
Maurice Funk ◽  
Jean Christoph Jung ◽  
Carsten Lutz
Keyword(s):  
Active Learning ◽  
Polynomial Time ◽  
Description Logic ◽  
Learning Algorithm ◽  
Domain Expert ◽  
Conjunctive Queries ◽  
Membership Queries ◽  
Equivalence Queries

We consider the problem to learn a concept or a query in the presence of an ontology formulated in the description logic ELr, in Angluin's framework of active learning that allows the learning algorithm to interactively query an oracle (such as a domain expert). We show that the following can be learned in polynomial time: (1) EL-concepts, (2) symmetry-free ELI-concepts, and (3) conjunctive queries (CQs) that are chordal, symmetry-free, and of bounded arity. In all cases, the learner can pose to the oracle membership queries based on ABoxes and equivalence queries that ask whether a given concept/query from the considered class is equivalent to the target. The restriction to bounded arity in (3) can be removed when we admit unrestricted CQs in equivalence queries. We also show that EL-concepts are not polynomial query learnable in the presence of ELI-ontologies.

scholarly journals Exact learning of juntas from membership queries

2018 ◽  
Vol 742 ◽  
pp. 82-97
Author(s):  
Nader H. Bshouty ◽  
Areej Costa
Keyword(s):  
Membership Queries ◽  
Exact Learning

scholarly journals The universality of polynomial time Turing equivalence

2016 ◽  
Vol 28 (3) ◽  
pp. 448-456 ◽  
Author(s):  
ANDREW MARKS
Keyword(s):  
Computational Complexity ◽  
Large Class ◽  
Complexity Theory ◽  
Polynomial Time ◽  
Equivalence Relations ◽  
Turing Degrees ◽  
Computational Complexity Theory ◽  
Borel Sets ◽  
Borel Equivalence Relations

We show that polynomial time Turing equivalence and a large class of other equivalence relations from computational complexity theory are universal countable Borel equivalence relations. We then discuss ultrafilters on the invariant Borel sets of these equivalence relations which are related to Martin's ultrafilter on the Turing degrees.

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