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Table 1 Experimental results for the identification of bifurcation transitions depending if \((\mathrm{I3})\) or \((\mathrm{I3}^\#)\) is used, compared to a exact model checking (MC) using NuSMV [20]

From: Identification of bifurcation transitions in biological regulatory networks using Answer-Set Programming

Automata network |States| Goal MC (NuSMV) With \((\mathrm{I3})\) With \((\mathrm{I3}^\#)\)
\(|t_b|\) Time (s) \(|t_b|\) Time (s) \(|t_b|\) Time (s)
Lambda phage \(|\Sigma |=4\quad |T|=11\) 14 \(\mathrm {CI}_2\) 10 0.1 6 0.1 0 0.2
\(\mathrm {Cro}_2\) 3 0.1 3 0.1 2 0.3
EGF/TNF \(|\Sigma |=28\quad |T|=55\) 3698 \(\mathrm {NFkB}_0\) 5 0.2 4 0.1 2 0.1
\(\mathrm {IKB}_1\) 5 0.2 3 0.1 2 0.1
Th_th1 \(|\Sigma |=101\quad |T|=381\) ≈3.1011 \(\mathrm {BCL6}_1\) 8 13 6 16 5 23
\(\mathrm {TBET}_1\) 11 14 5 10 4 24
Th_th2 \(|\Sigma |=101\quad |T|=381\) ≈1012 \(\mathrm {GATA3}_1\) 9 108 8 24 7 20
\(\mathrm {BCL6}_1\) 7 570 5 25 4 25
Th_pluri \(|\Sigma |=101\quad |T|=381\) >5.1014 BCL61 IL211 FOXP31 TGFB1 Out-of-time Out-of-time 2 32
0 26
4 56
5 96
  1. Models Th_th1, Th_th2, and Th_pluri are the same AN but have different initial states. \(|\Sigma |\) is the number of automata, and \(|T|\) the number of transitions; |states| is the number of reachable state from the initial state; in the case of Th_pluri, it is only a lower bound as we were not able to compute the full state space. \(|t_b|\) is the number of identified bifurcation transitions (among \(T\)). Computation times have been obtained on an Intel® Core™ i7-4770 3.40GHz CPU with 16GiB of RAM