Abstract
In this paper, we report how certain AI techniques can be used to speed up an algebraic algorithm for deciding the satisfiability of a system of polynomial equations, dis-equations, and inequalities. The algebraic algorithm (a restructured version of Cylindrical Algebraic Decomposition) is non-deterministic, in the sense that it can often achieve the same goal, but following different paths requiring different amounts of computing times. Obviously one wishes to follow the least time-consuming path. However, in practice it is not possible to determine such an optimal path. Thus it naturally renders itself to the heuristic search techniques of AI. In particular we experimented with Best-First strategy. The experimental results indicate that such AI techniques can often help in speeding up the algebraic method, sometimes dramatically.
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