Variants of P Systems with Toxic Objects

Abstract

Toxic objects have been introduced to avoid trap rules, especially in (purely) catalytic P systems. No toxic object is allowed to stay idle during a valid derivation in a P system with toxic objects. In this paper we consider special variants of toxic P systems where the set of toxic objects is prede ned { either by requiring all objects to be toxic or all catalysts to be toxic or all objects except the catalysts to be toxic. With all objects staying inside and being toxic, purely catalytic P systems cannot go beyond the nite sets, neither as generating nor as accepting systems. With allowing the output to be sent to the environment, exactly the regular sets can be generated. With non-cooperative systems with all objects being toxic we can generate exactly the Parikh sets of languages generated by extended Lindenmayer systems. Catalytic P systems with all catalysts being toxic can generate at least PsMAT.