# Linear Integer Arithmetic Revisited

arXiv: https://arxiv.org/abs/1503.02948 · HTML: https://mlsanity.com/paper/1503.02948/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Mar 2015.

## Built on by (most cited first, 1 of 1)

- [Constraint Answer Set Programming: Integrational and Translational (or SMT-based) Approaches](https://mlsanity.com/paper/2107.08252/) (2021)

## Abstract (arXiv)

We consider feasibility of linear integer programs in the context of verification systems such as SMT solvers or theorem provers. Although satisfiability of linear integer programs is decidable, many state-of-the-art solvers neglect termination in favor of efficiency. It is challenging to design a solver that is both terminating and practically efficient. Recent work by Jovanovic and de Moura constitutes an important step into this direction. Their algorithm CUTSAT is sound, but does not terminate, in general. In this paper we extend their CUTSAT algorithm by refined inference rules, a new type of conflicting core, and a dedicated rule application strategy. This leads to our algorithm CUTSAT++, which guarantees termination.