numeration system; recognizability; regular language; complexity function
Abstract :
[en] A generalization of numeration systems in which NI is recognizable by finite automata can be obtained by describing a lexicographically ordered infinite regular language. We show that if P is an element of Q[x] is a polynomial such that P(N) subset of N then there exists a numeration system in which the set of representations of P(N) is regular. The main issue is to construct a regular language with a complexity function equals to P(n + 1) - P(n) for n large enough. (C) 2002 Elsevier Science B.V. All rights reserved.
Disciplines :
Mathematics
Author, co-author :
Rigo, Michel ; Université de Liège - ULiège > Département de mathématique > Mathématiques discrètes
Language :
English
Title :
Construction of regular languages and recognizability of polynomials
scite shows how a scientific paper has been cited by providing the context of the citation, a classification describing whether it supports, mentions, or contrasts the cited claim, and a label indicating in which section the citation was made.
Bibliography
R.A. Brualdi, Introductory Combinatorics, North-Holland, New York-Oxford-Amsterdam, 1977.
V. Bruyère, G. Hansel, C. Michaux, R. Villemaire, Logic and p-recognizable sets of integers, Bull. Belg. Math. Soc. 1 (1994) 191-238.
O. Carton, W. Thomas, The monadic theory of morphic infinite words and generalizations, Mathematical Foundations of Computer Science 2000 (Bratislava), Lecture Notes in Computer Science, 1893, Springer, Berlin, 2000, pp. 275-284.
S. Eilenberg, Automata, Languages and Machines, Vol. A, Academic Press, New York, 1974.
C.H. Hardy, E.M. Wright, An Introduction to the Theory of Numbers, 4th Edition, Oxford University Press, Oxford, 1965.
P.B.A. Lecomte, M. Rigo, Numeration systems on a regular language, Theory Comput. Syst. 34 (2001) 27-44.
M. Rigo, Generalization of automatic sequences for numeration systems on a regular language, Theoret. Comp. Sci. 244 (2000) 271-281.
J. Shallit, Numeration systems, linear recurrences, and regular sets, Inform. Comput. 113(2) (1994) 331-347.
A. Szilard, S. Yu, K. Zhang, J. Shallit, Characterizing regular languages with polynomial densities, Proceedings of the 17th International Symposium on Mathematical Foundations of Computer Science, Lecture Notes in Computer Science, Vol. 629, Springer, Berlin, 1992, pp. 494-503.
Similar publications
Sorry the service is unavailable at the moment. Please try again later.
This website uses cookies to improve user experience. Read more
Save & Close
Accept all
Decline all
Show detailsHide details
Cookie declaration
About cookies
Strictly necessary
Performance
Strictly necessary cookies allow core website functionality such as user login and account management. The website cannot be used properly without strictly necessary cookies.
This cookie is used by Cookie-Script.com service to remember visitor cookie consent preferences. It is necessary for Cookie-Script.com cookie banner to work properly.
Performance cookies are used to see how visitors use the website, eg. analytics cookies. Those cookies cannot be used to directly identify a certain visitor.
Used to store the attribution information, the referrer initially used to visit the website
Cookies are small text files that are placed on your computer by websites that you visit. Websites use cookies to help users navigate efficiently and perform certain functions. Cookies that are required for the website to operate properly are allowed to be set without your permission. All other cookies need to be approved before they can be set in the browser.
You can change your consent to cookie usage at any time on our Privacy Policy page.
