Catalytic P Systems with Weak Priority of Catalytic Over Non-catalytic Rules

Catalytic P systems are among the rst variants of membrane systems ever considered in this area. This variant of systems also features some prominent computational complexity questions, and in particularly the problem of using only one catalyst: is one catalyst enough to allow for generating all recursively enumerable sets of multisets? Several additional ingredients have been shown to be su cient for obtaining even computational completeness with only one catalyst. In this paper we show that one catalyst is su cient for obtaining even computational completeness if catalytic rules have weak priority over the non-catalytic rules.