An Algebraic characterization of the affine three space in arbitrary characteristic

We give an algebraic characterization of the affine $3$-space over an algebraically closed field of arbitrary characteristic. We use this characterization to reformulate the following question. Let $$A=k[X,Y,Z,T]\mathrm{/}(XY+Z^{p^e}+T+T^{sp})$$ where $p^e\nmid sp$, $sp\nmid p^e$, $e,s\ge 1$ and $k$ is an algebraically closed field of positive characteristic $p$. Is $A=k^{[3]}$? We prove some results on ML and ML${}^{\ast }$ invariants and use them to prove a special case of the strong cancellation of $k^{[2]}$.