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Brzozowski`s conjecture: Start from any word w, and replace any occurrence uwn x by uwn 1 x or vice versa. Is the resulting language regular? This is easily seen...
Does every code have a unique primitive root? A set of words L is a code if every word has at most one factorization over L . For two languages L and R of words...
Let w be an infinite word generated (by iteration) by a given morphism. Let p be any rational number. If there exists a word u such that up is a factor of...
Fraenkel`s problem: A word is balanced if the number of occurrences of any letter in any two factors of equal length differ at most by 1. Given a k letter alphabet...
The Brown Freedman Halbeisen Hungerb...
Is Pi; Normal? A real number x is normal to base b if all finite words w over the alphabet {0,1, ..., b 1} occur as factors of the base b expansion of x with...
The Kolakoski word can be defined in a number of different ways, but probably the simplest is as the unique infinite word k over the alphabet {1, 2}, starting with...
What is the size of largest independent system of word equations? A system of word equations is independent if the set of solutions changes when any one equation...
Given two matrices, do they generate the free semigroup? The problem is open even for 2 2 integer matrices. A related result states that it is undecidable whether...
Nivat`s conjecture: Consider 2 dimensional words, that is, sets of letters indexed by Z2. Is the following conjecture true? If the number of distinct m ...
On the number of right special factors of a word. A factor u of a word w is right special if there exist two distinct letters a and b such that both ua and ub are...
Is PCP(3) decidable? The Post correspondence problem for lists of k words, called PCP(k), asks for a given set {(u1 , v1 ), . . . , (uk , vk )} of k pairs of words...
A finite word w is primitive if it is not a nontrivial power of another word, that is, if w uk for k 1 implies that k 1. Is the set of all primitive...
Reconstruction from subwords of given length: Determine the function f(n) k where k is the smallest integer for which the multiset of (scattered) subwords of...
The S adic conjecture: find the correct conditions on a sequence of morphisms so that an in #64257;nite word has linear complexity, if, and only if, it is generated...
What is the number of square free words? A word has a square if it contains two consecutive occurrences of the same factor. For an alphabet of size k 3, we ask for...
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Is deciding the satis #64257;ability of word equations in NP? This question is equivalent to asking whether one can check the correctness of a proposed solution of...
Is a given word k avoidable? A word x is called k avoidable if there exists an infinite word w over a k letter alphabet such that no morphic image of x occurs...
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