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Table 1 Brief description of the models used in our benchmarks

From: ASP-based method for the enumeration of attractors in non-deterministic synchronous and asynchronous multi-valued networks

Models Model description
\(|\Sigma |\) \(\max _{a\in \Sigma }\{|\mathcal {S}_a|\}\) \(|\mathcal {T}|\) \(|\mathcal {S}|\)
  Example 4 3 12 36
 [31] Lambda phage 4 4 46 48
 [32] Trp-reg 4 3 14 36
 [33] Fission-yeast 9 3 43 3 \(\times \) 2\(^\text {9}\) \(=\) 1536
 [34] Mamm. 10 2 34 2\(^{10}\) \(=\) 1024
 [35] Tcrsig 40 2 85 2\(^\text {40}\) \(\simeq \) 10\(^{12}\)
 [36] FGF 59 3 102 2\(^\text {31}\) \(\simeq \) 1.2 \(\times \) 10\(^\text {10}\)
 [37] T-helper 101 3 316 2\(^\text {102}\) \(\simeq \) 5.7 \(\times \) 10\(^\text {31}\)
  1. The successive lines sum up the information regarding the models of, respectively, the toy example of Fig. 1, the bacteriophage lambda [31], the tryptophan biosynthesis in E.coli regression [32], the fission yeast [33], the mammilian cell cycle [34], the TCR signalling pathway in the mammalian differentiation [35], the drosophila FGF signalling pathway [36] and the T-helper cell differentiation [37]. For each of them, the table gives the number of automata (\(|\Sigma |\)), the maximal local level in the automata (\(\max _{a\in \Sigma }\{|\mathcal {S}_a|\}\)), the number of local transitions (\(|\mathcal {T}|\)) and the number of states in the corresponding state-transition graph (\(|\mathcal {S}|\))