Efficient Generation of Test Data with Extended Cardinality Constraints

We present an extension of first-order logic that includes a counting quantifier, allowing one to express assertions about the number n of elements in a set that satisfy a given property. We show how this logic can be used to express problems such as node degree distribution in computer networks, various graph problems and entity relationships with cardinality constraints found in UML diagrams. We then present a translation of this counting logic back into classical first-order logic; this translation is linear in the number of quantifiers and independent of n. This translation makes it possible to use existing first-order model finders to efficiently generate test data following a specific distribution.