Red–Green P Automata

Abstract

Acceptance and recognizability of finite strings by red–green Turing machines are defined via infinite runs on the input string and the way how to distinguish between red and green states. We extend the notion of red–green Turing machines to register machines with an input tape and then to several variants of P automata. In order to allow for correct simulations of infinite computations of register machines, the models of P automata have to avoid trapping leading to unwanted infinite computations. Therefore, besides the original model of P automata using antiport rules we here consider two models introduced just recently and also allowing for deterministic simulations of register machine instructions, i.e., we consider the models of P systems with anti-matter as well as catalytic P systems with toxic objects. For all these models of P automata we define their red–green variants and show that they can simulate red–green register machines and therefore red–green Turing machines.