Techniques
This page is for listing all techniques applied by the participants of the complexity competitions.
Be aware: the lists are still preliminary.
Derivational Complexity
| Method | 2011 | 2010 | 2009 | 2008 | |
|---|---|---|---|---|---|
| Arctic Interpretation | CaT | CaT, TcT | CaT, TcT | CaT, TcT | |
| Match Bounds | CaT, TcT | CaT, TcT | CaT, TcT | CaT, TcT | |
| Matrix Interpretation Triangular | TcT (N) | TcT (N) | CaT (N), Matchbox (N), TcT (N) | TcT (N) | |
| Matrix Interpretation Non-Triangular | CaT (N,R,Q), Matchbox (N) | CaT (N,R,Q), Matchbox (N) | --- | --- | |
| Modular (Relative) Complexity Analysis | CaT | CaT | CaT | --- | |
| Rewriting Right Hand Sides | --- | --- | TcT | CaT | |
| Root Labeling | CaT | CaT | CaT, TcT | CaT | |
| Weight Gap Principle | CaT, TcT | CaT, TcT | CaT | --- |
Runtime Complexity
| Method | 2012 | 2011 | 2010 | 2009 | 2008 |
|---|---|---|---|---|---|
| Arctic Interpretation | CaT | CaT | CaT | CaT, TcT | --- |
| Match Bounds | AProVE, CaT, TcT | CaT, TcT | CaT, TcT | CaT, TcT | TcT |
| Matrix Interpretation Triangular | AProVE (N) | AProVE (N), TcT (N) | AProVE (N), TcT (N) | CaT (N), TcT (N) | TcT (N) |
| Matrix Interpretation Non-Triangular | CaT (N,R,Q), TcT (N) | CaT (N,R,Q) | CaT (N,R,Q) | --- | --- |
| Modular (Relative) Complexity Analysis | AProVE, CaT, TcT | AProVE, CaT | AProVE, CaT | CaT | --- |
| Polynomial Interpretations | AProVE (N), TcT (N) | AProVE (N) | AProVE (N) | --- | --- |
| Polynomial Path Orders | TcT (sPOP*) | TcT | TcT | TcT | TcT |
| Rewriting Right Hand Sides | AProVE | AProVE | AProVE | --- | --- |
| Root Labeling | --- | --- | --- | CaT, TcT | --- |
| Weak Dependency Pairs | TcT | TcT | TcT | TcT | TcT |
| Dependency Tuples | AProVE, TcT | AProVE, TcT | AProVE | --- | --- |
| Path Analysis | TcT | TcT | TcT | TcT | TcT |
| Weight Gap Principle | CaT, TcT | CaT, TcT | CaT, TcT | TcT | TcT |
| DG Decomposition | TcT | --- | --- | --- | --- |