Communications of the ACM
On the learnability of Boolean formulae
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Learning regular sets from queries and counterexamples
Information and Computation
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
Learning decision trees from random examples needed for learning
Information and Computation
Learning Nested Differences of Intersection-Closed Concept Classes
Machine Learning
Non-uniform automata over groups
Information and Computation
On learning embedded symmetric concepts
COLT '93 Proceedings of the sixth annual conference on Computational learning theory
Computational Complexity - Special issue on circuit complexity
Learning Behaviors of Automata from Multiplicity and Equivalence Queries
SIAM Journal on Computing
A simple algorithm for learning O (log n)-term DNF
Information Processing Letters
Learning functions represented as multiplicity automata
Journal of the ACM (JACM)
Machine Learning
Machine Learning
Machine Learning
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
Computational complexity questions related to finite monoids and semigroups
Computational complexity questions related to finite monoids and semigroups
Lower bounds for circuits with MOD_m gates
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Learning expressions and programs over monoids
Information and Computation
Languages with bounded multiparty communication complexity
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
The bacterial strains characterization problem
Proceedings of the 2011 ACM Symposium on Applied Computing
Learning read-constant polynomials of constant degree modulo composites
CSR'11 Proceedings of the 6th international conference on Computer science: theory and applications
Minimum multiple characterization of biological data using partially defined boolean formulas
Proceedings of the 27th Annual ACM Symposium on Applied Computing
| Hi-index | 0.00 |
In order to systematize existing results, we propose to analyze the learnability of boolean functions computed by an algebraically defined model, programs over monoids. The expressiveness of the model, hence its learning complexity, depends on the algebraic structure of the chosen monoid. We identify three classes of monoids that can be identified, respectively, from Membership queries alone, Equivalence queries alone, and both types of queries. The algorithms for the first class are new to our knowledge, while those for the other two are combinations or particular cases of known algorithms. Learnability of these three classes captures many previous learning results. Moreover, by using nontrivial taxonomies of monoids, we can argue that using the same techniques to learn larger classes of boolean functions seems to require proving new circuit lower bounds or proving learnability of DNF formulas.