castalia wrote:To determine the complexity of a technique, simply count the number of operations required to carry it out. If that number is proportional to a simple power of N, the complexity is polynomial; if it's some number to the Nth power, that makes the technique exponential.

Full backtracking is the best example of an exponential technique in sudoku. Limited backtracking (e.g. Nishio) can be polynomial, but doesn't always succeed. Looking for pairs is polynomial (proportional to N^2).

The presence of backtracking is perhaps the tell-tale sign of any trial and error (i.e. exponential) technique.

Thank you for the explanation. According to the definition above, is it appropriate to say that:

- "Trial" itself doesn't render a technique being T&E.
- All techniques that don't use backtracking as part of their identification processes are non-T&E, including all pattern recognition techniques such as BUG, swordfish, b/b plot, advanced colouring and POM.
- Techniques that use backtracking could be T&E or non-T&E, depending upon the degree of backtracking required. The degree of backtracking can be determined by the number of operations; as being polynomial or exponential.
- Forcing chain, by itself, cannot be considered as T&E or not, but techniques for identification of forcing chains could be T&E or non-T&E depending on the degree of backtracking. If this is the case, could you give an example each, techniques that you would consider T&E and non-T&E according to the above definition.

Thanks with anticipation.