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Conference Papers Year : 2016

Asynchronous simulation of Boolean networks by monotone Boolean networks

Abstract

We prove that the fully asynchronous dynamics of a Boolean network f : {0, 1}^n → {0, 1}^n without negative loop can be simulated, in a very specific way, by a monotone Boolean network with 2n components. We then use this result to prove that, for every even n, there exists a monotone Boolean network f : {0, 1}^n → {0, 1}^n , an initial configuration x and a fixed point y of f such that: (i) y can be reached from x with a fully asynchronous updating strategy, and (ii) all such strategies contains at least 2^{n/2} updates. This contrasts with the following known property: if f : {0, 1}^n → {0, 1}^n is monotone, then, for every initial configuration x, there exists a fixed point y such that y can be reached from x with a fully asynchronous strategy that contains at most n updates.
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Dates and versions

hal-01341136 , version 1 (04-07-2016)

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Cite

Tarek Melliti, Damien Regnault, Adrien Richard, Sylvain Sené. Asynchronous simulation of Boolean networks by monotone Boolean networks. Fourth International Workshop on Asynchronous Cellular Automata and Asynchronous Discrete Models, During the 12th International Conference on Cellular Automata for Research and Industry (ACRI 2016), Sep 2016, Fez, Morocco. pp.182--191, ⟨10.1007/978-3-319-44365-2_18⟩. ⟨hal-01341136⟩
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