Could anyone help me please to find who was the first person who has proved that the language of all borderless words is not regular and when was that? Could you mention the reference, please? A word ...
I know the answer without nesting limit is the Catalan number. My question is, specifically, is there a recurrence relation that gives the number of expression containing $n$ pairs of matching ...
I have one puzzle whose answer I have boiled down to finding the total number and which type of permutation they are. For example if the string is of length ten as $w = aabbbaabba$, the total number ...
This question has been prompted by Efficient data structures for building a fast spell checker. Given two strings $u,v$, we say they are $k$-close if their Damerau–Levenshtein distance¹ is small, ...
I want to count the number of strings $s$ over a finite alphabet $A$, that contain no repeats, and by that I mean for any substring $t$ of $s$, $1< |t| < |s|$, there is no disjoint copy of $t$ ...
Is there an algebraic characterization of the number of words of a given length in a regular language? Wikipedia states a result somewhat imprecisely: For any regular language $L$ there exist ...
According to Wikipedia, for any regular language $L$ there exist constants $\lambda_1,\ldots,\lambda_k$ and polynomials $p_1(x),\ldots,p_k(x)$ such that for every $n$ the number $s_L(n)$ of words of ...
Let $\Sigma$ be some finite set of characters of fixed size. Let $\alpha$ be some string over $\Sigma$. We say that a nonempty substring $\beta$ of $\alpha$ is a repeat if $\beta = \gamma \gamma$ for ...