On the power of membrane dissolution in polarizationless P systems with active membranes

It is known that dissolution rules are necessary in polarizationless P systems with active membranes to solve problems beyond AC0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {AC^0}$$\end{document} using reasonable tight uniformity conditions (Murphy and Woods, Fundam Inf Series 134:129–152, 2014). On the other hand, no solutions of such problems exist using only dissolution rules. In this paper, we show that the NL\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {NL}$$\end{document}-complete reachability problem can be solved in polynomial time by polarizationless P systems with active membranes using only dissolution rules under a suitable uniformity condition.