I'm currently looking for PhD and postdoc candidates. Contact me if you are interested.
Potential topics include:
Algorithmic theory of shuffle-finite series and its applications to combinatorics and control theory. Based on the works [1][2][3].
Zeroness of discrete and continuous-time polynomial control systems.
Solvability of systems of differential and difference equations.
First-order theory of univariate power series RINGS
First-order theory of univariate power series RINGS
This paper (entitled "A Decision Method for First-Order Stream Logic") claims a double-exponential decision procedure for the first-order theory of univariate power series, however it contains a flaw. The problem is known to be decidable. Is there an elementary decision procedure?