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We present a linear characterization for the solution sets of propositional calculus formulas in conjunctive normal form. We obtain recursive definitions for the linear characterization similar to the basic recurrence relation used to define binomial coefficients. As a consequence, we are able to use standard combinatorial and linear algebra techniques to describe properties of the linear characterization.
A modification of the ellipsoid algorithm is shown to be capable of testing for satisfiability a system of linear equations and inequalities with integer coefficients of the form Ax = b, x ≥ 0. All the rational arithmetic is performed exactly, without losing polynomiality of the computing time. In case of satisfiability, the approach always provides a rational feasible point. The bulk of the computations...
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