General plans regarding games.
More...
Go to the source code of this file.
Detailed Description
General plans regarding games.
 Todo:
 Connections
 Todo:
 Create milestones
 Todo:
 Generalising positional games to SAT

See "Positional games" in ComputerAlgebra/Hypergraphs/Lisp/plans/Colouring.hpp for the hypergraph versions.

The right generalisation of the nplayer versions seems to be as follows:

Given n clausesets F_1,...,F_n.

At the beginning the partial assignment phi to be constructed is empty.

A move of player i is to choose a yet unassigned variable v and a value e for it, and to extend phi by <v > e>

The winner is i who has first an empty clause in phi * F_i.

More precisely i wins iff it is his turn to move, and either there is already the empty clause in phi * F_i, or after his move the empty clause is in phi * F_i.

It seems important that the players are not associated with truth values.

So instead of boolean clausesets F_1,..., F_n we can also have generalised clausesets with nonboolean values  this just yields more choices for the players.

For a hypergraph G and n players the positional game on G, where every player has his own colour, is represented by the generalised clauseset representing the generalised colouring problem for n copies of G, where player i has the clauses using his colour. Here essentially there is no choice of truthvalue, since only the truth value i can falsify a literal in a clause of F_i.
Definition in file general.hpp.