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ON HIERARCHY OF THE POSITIONED ECO-GRAMMAR SYSTEMS WITH GIVEN NUMBERS OF AGENTS
Abstract
Eco-grammar systems represent grammar systems which were motivated by the behaviour of ecosystems. They were introduced in 1994 in order to describe evolving environment and community of agents together with the interplay among them. Positioned eco-grammar systems (PEG systems, for short) were introduced in our previous paper as a variant of the eco-grammar systems. Motivation for introducing the PEG systems and its main difference from the original eco-grammar systems is that we focus on the embodiment of the agents and their presence in the environment. Action of the agent is strictly determined by its position in the environment and by the symbol located immediately next to the position of the agent. PEG systems combine approaches known from the study of above mentioned eco-grammar systems and PM-colonies. PEG systems bring new view to the investigation of the interplay between the community of agents and the environment. Our approach allows studying local changes in evolving environment caused by agents. Moreover, the position of an agent is strictly given by the special symbol and we are able to predict its behaviour and control the evolution of the environment as well. Actions of agents have priority over the development of the environment and they are synchronized in totally parallel way. In this paper we extend already known results in hierarchy of PEG systems with respect to the number of agents present in the environment. As we already showed in [5] the generative power of PEG systems depends on the number of agents present in environment. We considered situation when there is at most ???0 agents present in the environment in each derivation step. We denote such systems ???????? and we showed that these systems form an infinite hierarchy ?????????????????+1. In this paper we are going to investigate hierarchy and generative power of PEG systems in the case where we consider strictly given number of agents present in environment; we denote this systems ??????!?? systems.
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