Learning One-Variable Pattern Languages Very Efficiently on Average, in Parallel, and by Asking Queries

A pattern is a string of constant and variable symbols. The language generated by a pattern is the set of all strings of constant symbols which can be obtained from by substituting non-empty strings for variables. We study the learnability of one-variable pattern languages in the limit with respect to the update time needed for computing a new single guess and the expected total learning time taken until convergence to a correct hypothesis. The results obtained are threefold. First, we design a consistent and set-driven learner that, using the concept of descriptive patterns, achieves update time O(n2 log n), where n is the size of the input sample. The best previously known algorithm to compute descriptive one-variable patterns requires time O(n4 log n) (cf. Angluin [1]). Second, we give a parallel version of this algorithm requiring time O(log n) and O(n3 / log n) processors on an EREW-PRAM. Third, we devise a one-variable pattern learner whose expected total learning time is O( 2 ...

• Type: Conference
• Year: 1997
• Where: ALT
• Authors: Thomas Erlebach, Peter Rossmanith, Hans Stadtherr, Angelika Steger, Thomas Zeugmann
• Keywords: ALT 1997, Machine Learning, One-variable Patterns, Total Learning Time, Update Time