Communications of the ACM
Learning regular sets from queries and counterexamples
Information and Computation
Finite monoids and the fine structure of NC1
Journal of the ACM (JACM)
Bounded-width polynomial-size branching programs recognize exactly those languages in NC1
Journal of Computer and System Sciences - 18th Annual ACM Symposium on Theory of Computing (STOC), May 28-30, 1986
Programs over aperiodic monoids
Theoretical Computer Science
Non-uniform automata over groups
Information and Computation
The membership problem in aperiodic transformation monoids
Journal of the ACM (JACM)
When won't membership queries help?
Selected papers of the 23rd annual ACM symposium on Theory of computing
Oracles and queries that are sufficient for exact learning
Journal of Computer and System Sciences
Learning Behaviors of Automata from Multiplicity and Equivalence Queries
SIAM Journal on Computing
Learning functions represented as multiplicity automata
Journal of the ACM (JACM)
Machine Learning
Machine Learning
An Algebraic Approach to Communication Complexity
ICALP '98 Proceedings of the 25th International Colloquium on Automata, Languages and Programming
On Learning Programs and Small Depth Circuits
EuroCOLT '97 Proceedings of the Third European Conference on Computational Learning Theory
Groupoids that recognize only regular languages
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Regular languages, unambiguous concatenation and computational complexity
FSTTCS'04 Proceedings of the 24th international conference on Foundations of Software Technology and Theoretical Computer Science
An algebraic view on exact learning from queries
CiE'05 Proceedings of the First international conference on Computability in Europe: new Computational Paradigms
Hi-index | 0.00 |
We study the problem of learning an unknown function represented as an expression over a known finite monoid. As in other areas of computational complexity where programs over algebras have been used, the goal is to relate the computational complexity of the learning problem with the algebraic complexity of the finite monoid. Indeed, our results indicate a close connection between both kinds of complexity. We focus on monoids which are either groups or aperiodic, and on the learning model of exact learning from queries. For a group G, we prove that expressions over G are easily learnable if G is nilpotent and impossible to learn efficiently (under cryptographic assumptions) if G is nonsolvable. We present some partial results for solvable groups, and point out a connection between their efficient learnability and the existence of lower bounds on their computational power in the program model. For aperiodic monoids, our results seem to indicate that the monoid class known as DA captures exactly learnability of expressions by polynomially many Evaluation queries.