13th International Conference on Membrane Computing - MTA Sztaki

H. ElGindy, R. Nicolescu, H. Wu
Table 1. Initial and final configurations of P Specification 1, for Figure 1.
Cell σ 0 σ 1 σ 2 σ 3
Initial S 0 ι 0 s S 0 ι 1 S 0 ι 2 S 0 ι 3
Final S 60 ι 0 s d ′′
1 d ′′
2 d ′′
3 S 60 ι 1 d ′ 0 d ′′
4 S 60 ι 2 d ′ 0 d ′′
6 S 60 ι 3 d ′ 0 d ′′
5
Cell σ 4 σ 5 σ 6 σ 7
Initial S 0 ι 4 S 0 ι 5 S 0 ι 6 S 0 ι 7 t
Final S 60 ι 4 d ′ 1 d ′′
7 S 60 ι 5 d ′ 3 d ′′
7 S 60 ι 6 d ′ 2 d ′′
7 S 60 ι 7 t d ′ 4 d ′ 5 d ′ 6
and k are free variables related to cell IDs, symbols X and Y are free variables
which match multisets; conventionally, we use i, j and k as subscripts and X
and Y as arguments.
0. Shared start (S 0 –S 2 )
0.1.
1. S 0 n → min.min S 1 (n)↕ ∀ (n ′′
i )↑ ∀ (n ′ i)↓ ∀ | ι i
2. S 0 → min S 0 n | s
0.2.
1. S 1 → min S 2
0.3.
1. S 2 n → max S 3
2. S 2 → min S 3
1. Initial differentiation (S 3 ): cf. Lines 3.4-7
1.1.
1. S 3 → min S 10 f r i(c) (w i v i)↕ ∀ | ι i s
2. S 3 → min S 30 | t
3. S 3 → min S 20
2. Source cell (S 10 ): cf. Lines 3.8-14, 7.15, 3.20-22
2.1.
1. S 10 f → min.min S 10 s ′′
k (f i r i(Xc))↓ k | n ′′
k h(X) ι i ¬ w k v k
2. S 10 a s ′′
k n ′′
k → min.min S 40 p d ′′
k (p)↕
3. S 10 a → max S 40
4. S 10 b k s ′′
k n ′′
k → min.min S 40 q (q)↕
5. S 10 b k → max.max S 40
6. S 10 f → min.min S 50 (g)↕
3. Intermediate cells (S 20 )
3.1. Finalisation: cf. Line 3.22
1. S 20 g → min.min S 50 (g)↕
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