About non-monotony in Boolean automata networks

International audienceThis paper aims at presenting motivations and rst results of a prospective theoretical study on the role of non-monotone interactions in the modelling process of biological regulation networks. Focusing on discrete models of these networks, namely, Boolean automata networks, we propose to analyse the contribution of non-monotony to the diversity and complexity in their dynamical behaviours. More precisely, in this paper, we start by detail- ing some motivations, both mathematical and biological, for our interest in non-monotony, and we discuss how it may account for phenomena that cannot be produced by monotony only. Then, to build some understanding in this direction, we show some preliminary results on the dynamical be- haviours of some speci c non-monotone Boolean automata networks called xor circulant networks

Boolean networks synchronism sensitivity and XOR circulant networks convergence time

In this paper are presented first results of a theoretical study on the role of non-monotone interactions in Boolean automata networks. We propose to analyse the contribution of non-monotony to the diversity and complexity in their dynamical behaviours according to two axes. The first one consists in supporting the idea that non-monotony has a peculiar influence on the sensitivity to synchronism of such networks. It leads us to the second axis that presents preliminary results and builds an understanding of the dynamical behaviours, in particular concerning convergence times, of specific non-monotone Boolean automata networks called XOR circulant networks.Comment: In Proceedings AUTOMATA&JAC 2012, arXiv:1208.249

A FINITE AXIOMATISATION OF FINITE-STATE AUTOMATA USING STRING DIAGRAMS

We develop a fully diagrammatic approach to finite-state automata, based on reinterpreting their usual state-transition graphical representation as a two-dimensional syntax of string diagrams. In this setting, we are able to provide a complete equational theory for language equivalence, with two notable features. First, the proposed axiomatisation is finite. Second, the Kleene star is a derived concept, as it can be decomposed into more primitive algebraic blocks

A Finite Axiomatisation of Finite-State Automata Using String Diagrams

We develop a fully diagrammatic approach to finite-state automata, based on reinterpreting their usual state-transition graphical representation as a two-dimensional syntax of string diagrams. In this setting, we are able to provide a complete equational theory for language equivalence, with two notable features. First, the proposed axiomatisation is finite. Second, the Kleene star is a derived concept, as it can be decomposed into more primitive algebraic blocks.Comment: arXiv admin note: text overlap with arXiv:2009.1457

Asynchronous simulation of Boolean networks by monotone Boolean networks

International audienceWe 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