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首页> 外文会议>WAINA 2010;IEEE International Conference on Advanced Information Networking and Applications Workshops >On the Number of Attractors of Positive and Negative Boolean Automata Circuits
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On the Number of Attractors of Positive and Negative Boolean Automata Circuits

机译：关于正负布尔自动机电路吸引子的数量

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摘要

In line with fields of theoretical computer science and biology that study Boolean automata networks often seen as models of regulation networks, we present some results concerning the dynamics of networks whose underlying interaction graphs are circuits, that is, Boolean automata circuits. In the context of biological regulation, former studies have highlighted the importance of circuits on the asymptotic dynamical behaviour of the biological networks that contain them. Our work focuses on the number of attractors of Boolean automata circuits. We prove how to obtain formally the exact value of the total number of attractors of a circuit of arbitrary size n as well as, for every positive integer p, the number of its attractors of period p depending on whether the circuit has an even or an odd number of inhibitions. As a consequence, we obtain that both numbers depend only on the parity of the number of inhibitions and not on their distribution along the circuit.
机译：与研究布尔自动机网络（通常被视为调节网络的模型）的理论计算机科学和生物学领域相一致，我们提出了一些有关网络动态的结果，这些网络的基础交互图是电路，即布尔自动机电路。在生物调节的背景下，以前的研究强调了电路对包含它们的生物网络的渐近动力学行为的重要性。我们的工作集中在布尔自动机电路吸引子的数量上。我们证明如何正式获得任意大小n的电路的吸引子总数的精确值，以及对于每个正整数p，其周期为p的吸引子数取决于电路是偶数还是偶数。奇数个抑制。结果，我们得到两个数仅取决于抑制数的奇偶性，而不取决于它们沿电路的分布。

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