8 problems

A word equation is an equation between words whose letters may include variables, and its satisfiability asks whether the variables can be assigned words so that the equation holds…

Plandowski–Laine conjecture. In the latter case, the equation has at most $3$ solutions.

Let a system of equations be a set of word equations, and call it independent if it is not equivalent to any proper subset. A system is constant-free when its equations contain onl…

Let a system of equations be a set of word equations, and call it independent if it is not equivalent to any proper subset. A solution is nonperiodic when it is not periodic. Consi…

Let WordEquations denote the decision problem of whether a word equation has a solution. The NP-completeness conjecture. WordEquations is conjectured to be NP-complete. The conject…

Let $u_1,dots,u_m$ be words, and consider the identity … The identity is required to hold for every $k<K$ but fail for $k=K$. Nonexistence conjecture for $K=4$. No such words…

Let a system of word equations be a set of equations between words over a finite alphabet, and call it independent if no equation is a consequence of the others. Ehrenfeucht's conj…

The totally decomposable word conjecture. The following are equivalent: $w$ is totally decomposable; $w$ is uniquely universal; $w$ is universal; and $w(X,A)=B$ has a solution in t…