Solving Satisfiability of Polynomial Formulas By SampleCell Projection
Abstract
A new algorithm for deciding the satisfiability of polynomial formulas over the reals is proposed. The key point of the algorithm is a new projection operator, called samplecell projection operator, custommade for ConflictDriven Clause Learning (CDCL)style search. Although the new operator is also a CAD (Cylindrical Algebraic Decomposition)like projection operator which computes the cell (not necessarily cylindrical) containing a given sample such that each polynomial from the problem is signinvariant on the cell, it is of singly exponential time complexity. The samplecell projection operator can efficiently guide CDCLstyle search away from conflicting states. Experiments show the effectiveness of the new algorithm.
 Publication:

arXiv eprints
 Pub Date:
 March 2020
 arXiv:
 arXiv:2003.00409
 Bibcode:
 2020arXiv200300409L
 Keywords:

 Computer Science  Logic in Computer Science;
 Computer Science  Artificial Intelligence;
 Computer Science  Symbolic Computation