# Algebraic Reasoning Meets Automata in Solving Linear Integer Arithmetic (Technical Report)

arXiv: https://arxiv.org/abs/2403.18995 · HTML: https://mlsanity.com/paper/2403.18995/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Mar 2024.

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

- [Deconstructing Subset Construction -- Reducing While Determinizing](https://mlsanity.com/paper/2505.10319/) (2025)

## Abstract (arXiv)

We present a new angle on solving quantified linear integer arithmetic based on combining the automata-based approach, where numbers are understood as bitvectors, with ideas from (nowadays prevalent) algebraic approaches, which work directly with numbers. This combination is enabled by a fine-grained version of the duality between automata and arithmetic formulae. In particular, we employ a construction where states of automaton are obtained as derivatives of arithmetic formulae: then every state corresponds to a formula. Optimizations based on techniques and ideas transferred from the world of algebraic methods are used on thousands of automata states, which dramatically amplifies their effect. The merit of this combination of automata with algebraic methods is demonstrated by our prototype implementation being competitive to and even superior to state-of-the-art SMT solvers.