Static and Dynamic Definitions

Note that ‘dynamic’ may also refer to play that helps the game develop.

A property of a go position or a similar aspect of the game may have a ’static’ or a ‘dynamic’ definition or both.
A static definition is one in terms on the shapes on the board.
A dynamic definition is one in terms of sequences of moves.
A static or dynamic property may refer to one with a static or (only) a dynamic definition respectively.

Examples of static and dynamic definitions

Examples of a static definitions are:

• Two points are adjacent if there is a line^[1] between them on the board.
• A chain is a maximal strictly connected set of points occupied by the same colour.

Examples of dynamic definitions are:

• A group is pass-alive if it cannot be captured by any sequence of legal moves by its opponent.
• A group is killable if it can be entirely captured, whatever replies its owner makes, if its opponent plays first and makes no mistakes.

Optimisation of dynamic to static definitions

A dynamic definition is usually costly to evaluate because backtracking is needed to read out all possible relevant sequences. A statically defined property, on the other hand, is often something a human player learns to recognise almost by visual intuition; a computer may need some iteration, but a small number of passes over the data usually suffices.

Sometimes a dynamic definition can be shown equivalent to a static definition; in this case it is often easier for a human and usually a lot more efficient for a computer to evaluate the static definition. A static definition can also be useful even if it only provides a partial test: it may only work when the property does not hold, or only when it does hold; it may be inconclusive in some cases but still save effort.

Examples of static tests for dynamic definitions

An example of equivalence is Benson's Theorem, saying that a group is pass-alive (dynamically defined) if and only if it satisfies his definition of unconditional life, which says that each chain in it has two true eyes in the group (statically defined).

An example of a partial static test is given by the nakade shapes: a group is killable if its eyespace has one of these forms.

Notes

[1] By a ‘line’ here we mean, of course, a segment from one intersection to the next.