Regular Article: Solution of the Boolean Markus驴Yamabe Problem
Advances in Applied Mathematics
Necessary conditions for multistationarity in discrete dynamical systems
Discrete Applied Mathematics
Static Analysis of Boolean Networks Based on Interaction Graphs: A Survey
Electronic Notes in Theoretical Computer Science (ENTCS)
From kernels in directed graphs to fixed points and negative cycles in Boolean networks
Discrete Applied Mathematics
About non-monotony in Boolean automata networks
Theoretical Computer Science
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Given a Boolean function F:{0,1}^n-{0,1}^n, and a point x in {0,1}^n, we represent the discrete Jacobian matrix of F at point x by a signed directed graph G"F(x). We then focus on the following open problem: Is the absence of a negative circuit in G"F(x) for every x in {0,1}^n a sufficient condition for F to have at least one fixed point? As result, we give a positive answer to this question under the additional condition that F is non-expansive with respect to the Hamming distance.