Keywords and Synonyms
Computational learning ; Machine learning ; Multiplicity automata ; Formal series; Boolean formulas; Multivariate polynomials
Problem Definition
This problem is concerned with the learnability of multiplicity automata in Angluin's exact learning model and applications to the learnability of functions represented by small multiplicity automata.
The Learning Model
It is the exact learning model [2]: Let f be a target function. A learning algorithm may propose to an oracle, in each step, two kinds of queries: membership queries (MQ) and equivalence queries (EQ). In a MQ it may query for the value of the function f on a particular assignment z. The response to such a query is the value f(z).Footnote 1 In a EQ it may propose to the oracle a hypothesis function h. If h is equivalent to fon all input assignments then the answer to the query is YES and the learning algorithm succeeds and halts. Otherwise, the answer to the equivalence query is NO and the algorithm...
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
If f is boolean this is the standard membership query.
- 2.
AÂ nondeterministic automata is unambiguous if for every \( { w \in\Sigma^* } \) there is at most one accepting path.
Recommended Reading
Angluin, D.: Learning regular sets from queries and counterexamples. Inf. Comput. 75, 87–106 (1987)
Angluin, D.: Queries and concept learning. Mach. Learn. 2(4), 319–342 (1988)
Beimel, A., Bergadano, F., Bshouty, N.H., Kushilevitz, E., Varricchio, S.: On the applications of multiplicity automata in learning. In: Proc. of the 37th Annu. IEEE Symp. on Foundations of Computer Science, pp. 349–358, IEEE Comput. Soc. Press, Los Alamitos (1996)
Beimel, A., Bergadano, F., Bshouty, N.H., Kushilevitz, E., Varricchio, S.: Learning Functions Represented as Multiplicity Automata. J. ACM 47, 506–530 (2000)
Beimel, A., Kushilevitz, E.: Learning boxes in high dimension. In: Ben-David S. (ed.) 3rd European Conf. on Computational Learning Theory (EuroCOLT '97), Lecture Notes in Artificial Intelligence, vol. 1208, pp. 3–15. Springer, Berlin (1997) Journal version: Algorithmica 22, 76–90 (1998)
Bergadano, F., Catalano, D., Varricchio, S.: Learning sat-k-DNF formulas from membership queries. In: Proc. of the 28th Annu. ACM Symp. on the Theory of Computing, pp. 126–130. ACM Press, New York (1996)
Bergadano, F., Varricchio, S.: Learning behaviors of automata from multiplicity and equivalence queries. In: Proc. of 2nd Italian Conf. on Algorithms and Complexity. Lecture Notes in Computer Science, vol. 778, pp. 54–62. Springer, Berlin (1994). Journal version: SIAM J. Comput. 25(6), 1268–1280 (1996)
Bergadano, F., Varricchio, S.: Learning behaviors of automata from shortest counterexamples. In: EuroCOLT '95, Lecture Notes in Artificial Intelligence, vol. 904, pp. 380–391. Springer, Berlin (1996)
Bisht, L., Bshouty, N.H., Mazzawi, H.: On Optimal Learning Algorithms for Multiplicity Automata. In: Proc. of 19th Annu. ACM Conf. Comput. Learning Theory, Lecture Notes in Computer Science. vol. 4005, pp. 184–198. Springer, Berlin (2006)
Blum, A., Khardon, R., Kushilevitz, E., Pitt, L., Roth, D.: On learning read-k-satisfy-j DNF. In: Proc. of 7th Annu. ACM Conf. on Comput. Learning Theory, pp. 110–117. ACM Press, New York (1994)
Bshouty, N.H.: Exact learning via the monotone theory. In: Proc. of the 34th Annu. IEEE Symp. on Foundations of Computer Science, pp. 302–311. IEEE Comput. Soc. Press, Los Alamitos (1993). Journal version: Inform. Comput. 123(1), 146–153 (1995)
Bshouty, N.H.: Simple learning algorithms using divide and conquer. In: Proc. of 8th Annu. ACM Conf. on Comput. Learning Theory, pp. 447–453. ACM Press, New York (1995). Journal version: Computational Complexity, 6, 174–194 (1997)
Bshouty, N.H., Tamon, C., Wilson, D.K.: Learning Matrix Functions over Rings. Algorithmica 22(1/2), 91–111 (1998)
Kushilevitz, E.: A simple algorithm for learning \( { O(\log n) } \)-term DNF. In: Proc. of 9th Annu. ACM Conf. on Comput. Learning Theory, pp 266–269, ACM Press, New York (1996). Journal version: Inform. Process. Lett. 61(6), 289–292 (1997)
Kushilevitz, E., Mansour, Y.: Learning decision trees using the Fourier spectrum. SIAM J. Comput. 22(6), 1331–1348 (1993)
Melideo, G., Varricchio, S.: Learning unary output two-tape automata from multiplicity and equivalence queries. In: ALT '98. Lecture Notes in Computer Science, vol. 1501, pp. 87–102. Springer, Berlin (1998)
Ohnishi, H., Seki, H., Kasami, T.: A polynomial time learning algorithm for recognizable series. IEICE Transactions on Information and Systems, E77-D(10)(5), 1077–1085 (1994)
Schapire, R.E., Sellie, L.M.: Learning sparse multivariate polynomials over a field with queries and counterexamples. J. Comput. Syst. Sci. 52(2), 201–213 (1996)
Valiant, L.G.: A theory of the learnable. Commun. ACM 27(11), 1134–1142 (1984)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag
About this entry
Cite this entry
Beimel, A., Bergadano, F., Bshouty, N., Kushilevitz, E., Varricchio, S. (2008). Learning Automata. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-30162-4_194
Download citation
DOI: https://doi.org/10.1007/978-0-387-30162-4_194
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-30770-1
Online ISBN: 978-0-387-30162-4
eBook Packages: Computer ScienceReference Module Computer Science and Engineering