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The number of distinct Dyck words with exactly n pairs of parentheses is the n-th Catalan number. Notice that the Dyck language of words with n parentheses pairs is equal to the union, over all possible k, of the Dyck languages of words of n parentheses pairs with k innermost pairs, as defined in
Given , there is a string of balanced parentheses that begins with more than left parentheses, so that will consist entirely of left parentheses. By repeating y {\displaystyle y} , a string can be produced that does not contain the same number of left and right parentheses, and so they cannot be balanced.
NOTE C does not specify a radix for float, double, and long double. An implementation can choose the representation of float, double, and long double to be the same as the decimal floating types. [2] Despite that, the radix has historically been binary (base 2), meaning numbers like 1/2 or 1/4 are exact, but not 1/10, 1/100 or 1/3.
The sequence of pushes and pops performed by Knuth's sorting algorithm as it sorts a stack-sortable permutation form a Dyck language: reinterpreting a push as a left parenthesis and a pop as a right parenthesis produces a string of balanced parentheses. Moreover, every Dyck string comes from a stack-sortable permutation in this way, and every ...
In theoretical computer science and formal language theory, a regular language (also called a rational language) [1] [2] is a formal language that can be defined by a regular expression, in the strict sense in theoretical computer science (as opposed to many modern regular expression engines, which are augmented with features that allow the recognition of non-regular languages).
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(Reuters) -The Louisiana Department of Health said on Friday it has detected the first presumptive positive human case of H5N1 bird flu infection in the U.S. state.
A balanced sequence has complexity function at most n+1. [13] A Sturmian word over a binary alphabet is one with complexity function n + 1. [14] A sequence is Sturmian if and only if it is balanced and aperiodic. [2] [15] An example is the Fibonacci word. [14] [16] More generally, a Sturmian word over an alphabet of size k is one with ...