In this paper we present polynomial-time algorithms that translate First-Order Logic (FOL) theories to smaller propositional encodings than achievable before in polynomial time. For example, we can sometimes reduce the number of propositions to O(|P | + |C|), or O(|P | · log |P |), for |P | predicates of arity k and |C| constant symbols. The guarantee depends on availability of some graphical s...

Smectic orders on curved substrates can be described by differential forms of rank one (1-forms), whose geometric meaning is the differential of the local phase field of density modulation. The exterior derivative of the 1-form is the local dislocation density. Elastic deformations are described by superposition of exact differential forms. Applying this formalism to study smectic order on a to...

We present new insights and algorithms for converting reasoning problems in monadic First-Order Logic (includes only 1place predicates) into equivalent problems in propositional logic. Our algorithms improve over earlier approaches in two ways. First, they are applicable even without the unique-names and domain-closure assumptions, and for possibly infinite domains. Therefore, they apply for ma...