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Topology and Non-Deterministic Polynomial Time Computation : Avoidance of The Misbehaviour of Hub-Free Diagrams and Consequences

To study groups with small Dehn's function, Olshanskii and Sapir developed a new invariant of bipartite chords diagrams and applied it to hub-free realization of S-machines. In this paper we consider this new invariant together with groups constructed from S-machines containing the hub relation. The idea is to study the links between the topology of the asymptotic cones and polynomial time computations. Indeed it is known that the topology of such metric space depends on diagrams without hubs that do not correspond to the computations of the considered S-machine. This work gives sufficient conditions that avoid this misbehaviour, but as we shall see the method has a significant drawback.