The scope of this paper is the construction of Hierarchical Genetic Strategy theoretical model based on the L-systems framework. The model was defined in the case of inactive prefix comparison procedure of HGS. We applied Vose's theory in a short formal analysis of basic search mechanisms implemented in the strategy.
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Two special cases of eco-grammar systems are studied, namely the systems with identical agents, called monocultures and the systems with homogeneous environment characterized by a unary alphabet. The generative power of these eco-grammar systems, given by the languages of the environments, is discussed. Introduced special cases restrict the generative power of eco-grammar systems. Hierarchy or incomparability of language classes with respect to the degree of eco-grammar systems, given by the number of the agents, is shown for various cases of eco-grammar systems.
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In its initial presentation, the P system formalism describes the topology of the membranes as a set of nested regions. In this paper, we present an algebraic structure developped in combinatorial topology that can be used to describe finer adjacency relationships between membranes. Using an appropriate abstract setting, this technical device enables us to reformulate also the computation within a membrane and proposes a unified view on several computational mechanisms initially inspired by biological processes. These theoretical tools are instantiated in MGS, an experimental programming language handling various types of membrane structures in a homogeneous and uniform syntax.
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