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A functional defined on the class of generalized characteristic functions (fuzzy sets), called "entropy", is introduced using no probabilistic concepts in order to obtain a global measure of the indefiniteness connected with the situations described by fuzzy sets. This "entropy" may be regarded as a measure of a quantity of information which is not(More)
We prove some new results concerning the structure, the combinatorics and the arithmetics of the set PER of all the words w having two periods p and q, p <q, which are coprimes and such that ]w] = pfq-2. A basic theorem relating PER with the set of finite standard Sturmian words was proved in de Luca and Mignosi (1994). The main result of this paper is the(More)
We prove some new combinatorial properties of the set PER of all words w having two periods p and q which are coprimes and such that w = p + q-2 [4,3]. We show that aPERb U {a, b} = St n Lynd, where St is the set of the finite factors of all infinite Sturmian words and Lynd is the set of the Lyndon words on the alphabet {a, b}. It is also shown that aPERb U(More)
We consider involutory antimorphisms ϑ of a free monoid A * and their fixed points, called ϑ-palindromes or pseudopalindromes. A ϑ-palindrome reduces to a usual palindrome when ϑ is the reversal operator. For any word w ∈ A * the right (resp. left) ϑ-palindrome closure of w is the shortest ϑ-palindrome having w as a prefix (resp. suffix). We prove some(More)
In this paper we solve some open problems related to (pseudo)pal-indrome closure operators and to the infinite words generated by their iteration, that is, standard episturmian and pseudostandard words. We show that if ϑ is an involutory antimorphism of A * , then both ϑ-palindromic closures of any factor of a ϑ-standard word are also factors of some(More)
In this paper we consider the following question in the spirit of Ramsey theory: Given x ∈ A ω , where A is a finite non-empty set, does there exist a finite coloring of the non-empty factors of x with the property that no factorization of x is monochromatic? We prove that this question has a positive answer using two colors for almost all words relative to(More)