Symbolic Computation Techniques in Satisfiability Checking

Satisfiability Checking is a relatively young research area, aiming at the development of efficient software technologies for checking the satisfiability of existentially quantified logical formulas. Besides the success story of SAT solving for propositional logic, SAT-modulo-theories (SMT) solvers offer sophisticated solutions for different theories. When targeting arithmetic theories, SMT solvers also make use of decision procedures rooted in Symbolic Computation. In this paper we give a brief introduction to SMT solving, discuss differences to Symbolic Computation, and illustrate the potentials and obstacles for embedding Symbolic Computation techniques in SMT solving on the example of the Cylindrical Algebraic Decomposition.