DocumentCode :
2645083
Title :
On the applications of multiplicity automata in learning
Author :
Beimel, Amos ; Bergadano, F. ; Bshouty, N.H. ; Kushilevitz, Eyal ; Varricchio, S.
Author_Institution :
Dept. of Comput. Sci., Technion-Israel Inst. of Technol., Haifa, Israel
fYear :
1996
fDate :
14-16 Oct 1996
Firstpage :
349
Lastpage :
358
Abstract :
The learnability of multiplicity automata has attracted a lot of attention, mainly because of its implications on the learnability of several classes of DNF formulae. The authors further study the learnability of multiplicity automata. The starting point is a known theorem from automata theory relating the number of states in a minimal multiplicity automaton for a function f to the rank of a certain matrix F. With this theorem in hand they obtain the following results: a new simple algorithm for learning multiplicity automata with a better query complexity. As a result, they improve the complexity for all classes that use the algorithms of Bergadano and Varricchio (1994) and Ohnishi et al. (1994) and also obtain the best query complexity for several classes known to be learnable by other methods such as decision trees and polynomials over GF(2). They prove the learnability of some new classes that were not known to be learnable before. Most notably, the class of polynomials over finite fields, the class of bounded-degree polynomials over infinite fields, the class of XOR of terms, and a certain class of decision trees. While multiplicity automata were shown to be useful to prove the learnability of some subclasses of DNF formulae and various other classes, they study the limitations of this method. They prove that this method cannot be used to resolve the learnability of some other open problems such as the learnability of general DNF formulae or even K-term DNF for k=ω (log n) or satisfy-s DNF formulae for s=ω(1). These results are proven by exhibiting functions in the above classes that require multiplicity automata with superpolynomial number of states
Keywords :
automata theory; computational complexity; learning (artificial intelligence); matrix algebra; polynomials; DNF formulae learnability; automata theory; decision trees; finite field polynomials; infinite field bounded-degree polynomials; matrix; minimal multiplicity automaton; multiplicity automata; multiplicity automata learning; query complexity; states; Computer science; Learning automata; Polynomials; Postal services;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Foundations of Computer Science, 1996. Proceedings., 37th Annual Symposium on
Conference_Location :
Burlington, VT
ISSN :
0272-5428
Print_ISBN :
0-8186-7594-2
Type :
conf
DOI :
10.1109/SFCS.1996.548494
Filename :
548494
Link To Document :
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