The use of Craig interpolants has enabled the development of powerful hardware and software model checking techniques. Efficient algorithms are known for computing interpolants in rational and real linear arithmetic. We focus on subsets of integer linear arithmetic. Our main results are polynomial time algorithms for obtaining proofs of unsatisfiability and interpolants for conjunctions of line...

Since for interesting parameters these Diophantine linear systems are quite big and can not be solved by contemporary computer methods, we further reduce the size of the system by restricting the search to codes with a prescribed group of automorphisms, see also [1]. Then, in many cases the resulting systems can be solved by algorithms for lattice point enumeration [4]. With this approach many ...