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Full-Text Articles in Physical Sciences and Mathematics
Verifying Properties Of Neural Networks, Pedro Rodriques, J. Félix Costa, Hava Siegelmann
Verifying Properties Of Neural Networks, Pedro Rodriques, J. Félix Costa, Hava Siegelmann
Hava Siegelmann
In the beginning of nineties, Hava Siegelmann proposed a new computational model, the Artificial Recurrent Neural Network (ARNN), and proved that it could perform hypercomputation. She also established the equivalence between the ARNN and other analog systems that support hypercomputation, launching the foundations of an alternative computational theory. In this paper we contribute to this alternative theory by exploring the use of formal methods in the verification of temporal properties of ARNNs. Based on the work of Bradfield in verification of temporal properties of infinite systems, we simplify his tableau system, keeping its expressive power, and show that it is …
Symbolic Dynamics And Computation In Model Gene Networks, R. Edwards, Hava Siegelmann, K. Aziza, L. Glass
Symbolic Dynamics And Computation In Model Gene Networks, R. Edwards, Hava Siegelmann, K. Aziza, L. Glass
Hava Siegelmann
We analyze a class of ordinary differential equations representing a simplified model of a genetic network. In this network, the model genes control the production rates of other genes by a logical function. The dynamics in these equations are represented by a directed graph on an n-dimensional hypercube (n-cube) in which each edge is directed in a unique orientation. The vertices of the n-cube correspond to orthants of state space, and the edges correspond to boundaries between adjacent orthants. The dynamics in these equations can be represented symbolically. Starting from a point on the boundary between neighboring orthants, the equation …