When Less Is More: Consequence-Finding in a Weak Theory of Arithmetic

This paper presents a theory of non-linear integer/real arithmetic and algorithms for reasoning about this theory. The can be conceived as an extension linear with weakly-axiomatized multiplication symbol, which retains many the desirable algorithmic properties arithmetic. In particular, we show that conjunctive fragment effectively manipulated (analogously to usual operations on convex polyhedra, arithmetic). As result, solve following consequence-finding problem: given ground formula F , find strongest is entailed by . application consequence-finding, give loop invariant generation algorithm monotone respect (in sense) complete. Experiments invariants generated from consequences are effective proving safety programs require reasoning.