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Introducing perfectly nested circuits

Abstract:

Nested graphs have been used in different applications, for example to represent knowledge in semantic networks. On the other hand, graphs with cycles are really important in surface reconstruction, periodic schedule and network analysis. Also, of particular interest are the cycle basis, which arise in mathematical and algorithm problems. In this work we develop the concept of perfectly nested circuits, exploring some of their properties. The main result establishes an order isomorphism between some sets of perfectly nested circuits and equivalence classes over finite binary sequences. This main result could be useful for analizing binary sequences. As a particular case of nested graphs, PCNs could be useful in applications where general nested graphs are used; and this is in the immediate future of this research.