Cross-bifix-free sets in two dimensions
نویسندگان
چکیده
A bidimensional bifix (in short bibifix ) of a square matrix T is a square submatrix of T which occurs in the top-left and bottomright corners of T . This allows us to extend the definition of bifix-free words and cross-bifix-free set of words to bidimensional structures. In this paper we exhaustively generate all the bibifix -free square matrices and we construct a particular non-expandable cross-bibifix -free set of square matrices. Moreover, we provide a Gray code for listing this set.
منابع مشابه
A Gray Code for cross-bifix-free sets
A cross-bifix-free set of words is a set in which no prefix of any length of any word is the suffix of any other word in the set. A construction of cross-bifix-free sets has recently been proposed by Chee et al. in 2013 within a constant factor of optimality. We propose a trace partitioned Gray code for these cross-bifix-free sets and a CAT algorithm generating it.
متن کاملConstruction of Non-expandable Non-overlapping Sets of Pictures
The non-overlapping sets of pictures are sets such that no two pictures in the set (properly) overlap. They are the generalization to two dimensions of the cross-bifix-free sets of strings. Non-overlapping sets of pictures are non-expandable when no other picture can be added without violating the property. We present a construction of non-expandable non-overlapping (NENO) sets of pictures and ...
متن کاملBifix codes and Sturmian words
We study bifix codes in factorial sets of words. We generalize most properties of ordinary maximal bifix codes to bifix codes maximal in a recurrent set F of words (F -maximal bifix codes). In the case of bifix codes contained in Sturmian sets of words, we obtain several new results. Let F be a Sturmian set of words. Our results express the fact that an F -maximal bifix code of degree d behaves...
متن کاملThe finite index basis property
We describe in this paper a connection between bifix codes, symbolic dynamical systems and free groups. This is in the spirit of the connection established previously for the symbolic systems corresponding to Sturmian words. We introduce a class of sets of factors of an infinite word with linear factor complexity containing Sturmian sets and regular interval exchange sets, namely the class of t...
متن کاملAcyclic, connected and tree sets
Given a set S of words, one associates to each word w in S an undirected graph, called its extension graph, and which describes the possible extensions of w in S on the left and on the right. We investigate the family of sets of words defined by the property of the extension graph of each word in the set to be acyclic or connected or a tree. We exhibit for this family various connexions between...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Theor. Comput. Sci.
دوره 664 شماره
صفحات -
تاریخ انتشار 2017