Department of Computer Science, Lamar University, Beaumont, TX 77710, USA.
Adv Exp Med Biol. 2011;696:113-22. doi: 10.1007/978-1-4419-7046-6_12.
We present a computational method in which modular and Groebner bases (GB) computation in Boolean rings are used for solving problems in Boolean gene regulatory networks (BN). In contrast to other known algebraic approaches, the degree of intermediate polynomials during the calculation of Groebner bases using our method will never grow resulting in a significant improvement in running time and memory space consumption. We also show how calculation in temporal logic for model checking can be done by means of our direct and efficient Groebner basis computation in Boolean rings. We present our experimental results in finding attractors and control strategies of Boolean networks to illustrate our theoretical arguments. The results are promising. Our algebraic approach is more efficient than the state-of-the-art model checker NuSMV on BNs. More importantly, our approach finds all solutions for the BN problems.
我们提出了一种计算方法，该方法在布尔环中使用模块化和 Groebner 基（GB）计算来解决布尔基因调控网络（BN）中的问题。与其他已知的代数方法不同，在使用我们的方法计算 Groebner 基时，中间多项式的度数永远不会增加，从而显著提高了运行时间和内存空间的消耗。我们还展示了如何通过我们在布尔环中的直接和有效的 Groebner 基计算来进行模型检查中的时态逻辑计算。我们通过找到吸引子和布尔网络的控制策略来展示我们的理论论点，给出了实验结果。结果是有希望的。我们的代数方法在 BN 上比最先进的模型检查器 NuSMV 更有效。更重要的是，我们的方法找到了 BN 问题的所有解决方案。
