Title :
Learning DNF by approximating inclusion-exclusion formulae
Author :
Tarui, Jun ; Tsukiji, Tatsuie
Author_Institution :
Dept. of Commun. & Syst., Univ. of Electro-Commun., Tokyo, Japan
Abstract :
We analyze upper and lower bounds on size of Boolean conjunctions necessary and sufficient to approximate a given DNF formula by accuracy slightly better than 1/2 (here we define the size of a Boolean conjunction as the number of distinct variables on which it depends). Such an analysis determines the performance of a naive search algorithm that exhausts Boolean conjunctions in the order of their sizes. In fact, our analysis does not depend on kinds of symmetric functions to be exhausted: instead of conjunctions, counting either disjunctions, parity functions, majority functions, or even general symmetric functions, derives the same learning results from similar analyses
Keywords :
Boolean functions; learning (artificial intelligence); Boolean conjunctions; DNF learning; inclusion-exclusion formulae approximation; lower bounds; majority functions; parity functions; upper bounds; Accuracy; Algorithm design and analysis; Circuits; Informatics; Performance analysis; Polynomials; Random variables; Structural engineering; Upper bound;
Conference_Titel :
Computational Complexity, 1999. Proceedings. Fourteenth Annual IEEE Conference on
Conference_Location :
Atlanta, GA
Print_ISBN :
0-7695-0075-7
DOI :
10.1109/CCC.1999.766279