An Optimal Parallel Algorithm for Learning DFA
Дата
Авторы
Balcázar,José
Díaz,Josep
Gavaldà,Ricard
Watanabe,Osamu
Journal Title
Journal ISSN
Volume Title
Издатель
Journal of Universal Computer Science
Аннотация
Описание
Sequential algorithms given by Angluin (1987) and Schapire (1992) learn deterministic finite automata (DFA) exactly from Membership and Equivalence queries. These algorithms are feasible, in the sense that they take time polynomial in n and m, where n is the number of states of the automaton and m is the length of the longest counterexample to an Equivalence query. This paper studies whether parallelism can lead to substantially more efficient algorithms for the problem. We show that no CRCW PRAM machine using a number of processors polynomial in n and m can identify DFA in o(n/log n) time. Furthermore, this lower bound is tight up to constant factors: we develop a CRCW PRAM learning algorithm that uses polynomially many processors and exactly learns DFA in time O(n/log n).
Ключевые слова
computational learning theory , query learning , membership query , equivalence query , DFA , optimal parallel learning