Identification of unions of languages drawn from an identifiable class
COLT '89 Proceedings of the second annual workshop on Computational learning theory
The correct definition of finite elasticity: corrigendum to identification of unions
COLT '91 Proceedings of the fourth annual workshop on Computational learning theory
Learning algebraic structures from text
Theoretical Computer Science - Algorithmic learning theory
Mathematics based on incremental learning: excluded middle and inductive inference
Theoretical Computer Science - Algorithmic learning theory(ALT 2002)
Inferability of closed set systems from positive data
JSAI'06 Proceedings of the 20th annual conference on New frontiers in artificial intelligence
Learning Bounded Unions of Noetherian Closed Set Systems Via Characteristic Sets
ICGI '08 Proceedings of the 9th international colloquium on Grammatical Inference: Algorithms and Applications
Inferability of unbounded unions of certain closed set systems
JSAI-isAI'09 Proceedings of the 2009 international conference on New frontiers in artificial intelligence
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The surprising fact that Hilbert's basis theorem in algebra shows identifiabilty of ideals of polynomials in the limit from positive data is derived by the correspondence between ideals and languages in the context of machine learning. This correspondence also reveals the difference between the two and raises new problems to be solved in both of algebra and machine learning. In this article we solve the problem of providing a concrete form of the characteristic set of a union of two polynomial ideals. Our previous work showed that the finite basis of every polynomial ideal is its characteristic set, which ensures that the class of ideals of polynomials is identifiable from positive data. Union or settheoretic sum is a basic set operation, and it could be conjectured that there is some effective method which produces a characteristic set of a union of two polynomial ideals if both of the basis of ideals are given. Unfortunately, we cannot find a previous work which gives a general method for how to find characteristic sets of unions of languages even though the languages are in a class identifiable from positive data. We give methods for computing a characteristic set of the union of two polynomial ideals.