Revisiting Shinohara's algorithm for computing descriptive patterns
Henning Fernau
Florin Manea
Robert Mercas
Markus L. Schmid
2134/24634
https://repository.lboro.ac.uk/articles/journal_contribution/Revisiting_Shinohara_s_algorithm_for_computing_descriptive_patterns/9401570
A pattern α is a word consisting of constants and variables and it describes the pattern language L(α) of all words that can be obtained by uniformly replacing the variables with constant words. In 1982, Shinohara presents an algorithm that computes a pattern that is descriptive for a finite set S of words, i.e., its pattern language contains S in the closest possible way among all pattern languages. We generalise Shinohara’s algorithm to subclasses of patterns and characterise those subclasses for which it is applicable. Furthermore, within this set of pattern classes, we characterise those for which Shinohara’s algorithm has a polynomial running time (under the assumption P 6= N P). Moreover, we also investigate the complexity of the consistency problem of patterns, i.e., finding a pattern that separates two given finite sets of words.
2017-04-05 09:15:37
Pattern languages
Inductive inference
Descriptive patterns
N P-hard problems 2010 MSC: 68Q25, 68Q17, 68Q32