Table 1 Classified rewriting rules with respect to isomorphism levels
From: Structure sensitive complexity for symbol-free sequences
Class | Homomorphism | Isomorphism-1 | Isomorphism-2 |
|---|---|---|---|
1 | p ↦ Plr | p ↦ Plr | p ↦ Plr |
Pl ↦ Llr | |||
Pr ↦ Rlr | |||
2 | PLl ↦ L(1)lr | Pl ↦ Llr | Pl ↦ Llr |
PRl ↦ L(1) | Pr ↦ Rlr | ||
3 | PLr ↦ R(2) | PLl ↦ L(1)lr | Pr ↦ Rlr |
PRr ↦ R(2)lr | |||
4 | PLLl ↦ L(3) PRRl ↦ L(3) | PLr ↦ R(2) | PLl ↦ L(1)lr |
5 | PLLr ↦ R(4) PRRr ↦ R(4) | PRl ↦ L(1) | PLr ↦ R(2) |
6 | PRr ↦ R(2)lr | PRl ↦ L(1) | |
7 | PLLl ↦ L(3) | PRr ↦ R(2)lr | |
PRRl ↦ L(3) | |||
8 | PLLr ↦ R(4) | PLLl ↦ L(3) | |
PRRr ↦ R(4) | PRRl ↦ L(3) | ||
9 | PLLr ↦ R(4) | ||
PRRr ↦ R(4) |