Abstract
The syntactic inference problem consists of deciding, for a given set of words, whether there exists a grammar such that its language includes these given words; and also of actually finding any such grammars. In this paper, the problem is considered for DOL-systems. The stress is on the second, constructive, part of the problem. The initial information may have various forms. Most of the results deal with cases in which
— the words are given as a sequence (i.e., with their rank order numbers), which may be either consecutive or scattered.
— the size of the alphabet is given.
From the decidability point of view most of the results are not new. The proposed decision method, however, represents a considerable speed-up by passing the initial data through a number of algebraic "sieves" which turn out to be quite dense.
The method depends on there being enough information to establish a linear dependence relation between the Parikh-vectors of the given words.
Several variants of the problem are discussed. One subcase of a hitherto open problem is solved; other problems remain open.
Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
References
F.R. Gantmacher, The theory of matrices. New York: Chelsea, 1959 (Translated from the Russian).
G. Birkhoff and S. Maclane. A survey of modern algebra. New York: Mac Millan, 1953.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1974 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Doucet, P.G. (1974). The syntactic inference problem for dol-sequences. In: Rozenberg, G., Salomaa, A. (eds) L Systems. Lecture Notes in Computer Science, vol 15. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-06867-8_12
Download citation
DOI: https://doi.org/10.1007/3-540-06867-8_12
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-06867-9
Online ISBN: 978-3-540-37823-5
eBook Packages: Springer Book Archive