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)
Finite automata, formal logic, and circuit complexity
Finite automata, formal logic, and circuit complexity
When won't membership queries help?
Selected papers of the 23rd annual ACM symposium on Theory of computing
Superlinear lower bounds for bounded-width branching programs
Journal of Computer and System Sciences
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
Over words, two variables are as powerful as one quantifier alternation
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Learning functions represented as multiplicity automata
Journal of the ACM (JACM)
Automata, Languages, and Machines
Automata, Languages, and Machines
The complexity of solving equations over finite groups
Information and Computation
Machine Learning
Machine Learning
An Algebraic Approach to Communication Complexity
ICALP '98 Proceedings of the 25th International Colloquium on Automata, Languages and Programming
Algebraic Characterizations of Small Classes of Boolean Functions
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
Learning decision lists and trees with equivalence-queries
EuroCOLT '95 Proceedings of the Second European Conference on Computational Learning Theory
On Learning Programs and Small Depth Circuits
EuroCOLT '97 Proceedings of the Third European Conference on Computational Learning Theory
Simple PAC Learning of Simple Decision Lists
ALT '95 Proceedings of the 6th International Conference on Algorithmic Learning Theory
An algebraic perspective on Boolean function learning
ALT'09 Proceedings of the 20th international conference on Algorithmic learning theory
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We study the problem of learning an unknown function represented as an expression or a program 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 efficiently learnable if G is nilpotent, and impossible to learn efficiently (under cryptographic assumptions) if G is nonsolvable. We present some results for restricted classes of 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. When using programs instead of expressions, we show that our results for groups remain true, while the situation is quite different for aperiodic monoids.