Adaptive Solving of Equations over Rational Trees

Abstract

The solution of Dynamic Constraint Satisfaction Problems (DCSPs) in Constraint Logic Programming (CLP) basically requires a solution of dynamically changing systems of syntactical equations over the rational trees

For instance, let U; V;X; Y;Z be variables, c be a constant, f; g be function symbols and fX: = f(X; Y ); f(Z; c): = X;U: = V; V: = U; g(c): = Zg be a set of syntactical equations. Suppose that all but the last equations are considered and the rational solved form X: = f(X; Y ); Z: = f(X; Y ); Y: = c; U: = V: is calculated. Given the last equation, inconsistency is detected, because the two equations g(c): = Z and Z: = f(X; Y ) are unsolvable. For an adaptation of the rational solved form and the decision about the consistency after the deletion of the equation f(Z; c): = X in CLP we have the opportunity to backtrack to the first equation X: = f(X; Y ) and then recalculate the solution. A closer examination shows that backtracking is not really necessary. Only the bindings Z: = f(X; Y ) and Y: = c depend on the deleted equation. The binding U: = V and the equation V: = U are completely independent. Thus, for an adaptation it is sufficient to keep the bindings X = f(X; Y ); U: = V and reconsider the equation g(c): = Z

Based on this deeper understanding we developed an unification algorithm, which uses truth maintenance techniques to maintain a solved form of a set of equations over the rational trees.

The full paper is available at ftp://ftp.first.gmd.de/pub/plan/cp98-wolf.ps.