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EN
A topological property or index of a network is a numeric number which characterises the whole structure of the underlying network. It is used to predict the certain changes in the bio, chemical and physical activities of the networks. The 4-layered probabilistic neural networks are more general than the 3-layered probabilistic neural networks. Javaid and Cao [Neural Comput. and Applic., DOI 10.1007/s00521-017-2972-1] and Liu et al. [Journal of Artificial Intelligence and Soft Computing Research, 8(2018), 225-266] studied the certain degree and distance based topological indices (TI’s) of the 3-layered probabilistic neural networks. In this paper, we extend this study to the 4-layered probabilistic neural networks and compute the certain degree-based TI’s. In the end, a comparison between all the computed indices is included and it is also proved that the TI’s of the 4-layered probabilistic neural networks are better being strictly greater than the 3-layered probabilistic neural networks.
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Content available remote Parikh Matrices and Parikh Rewriting Systems
EN
Since the introduction of the Parikh matrix mapping, its injectivity problem is on top of the list of open problems in this topic. In 2010 Salomaa provided a solution for the ternary alphabet in terms of a Thue system with an additional feature called counter. This paper proposes the notion of a Parikh rewriting system as a generalization and systematization of Salomaa’s result. It will be shown that every Parikh rewriting system induces a Thue system without counters that serves as a feasible solution to the injectivity problem.
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