# SAT Modulo Monotonic Theories

arXiv: https://arxiv.org/abs/1406.0043 · HTML: https://mlsanity.com/paper/1406.0043/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 May 2014.

## Built on by (most cited first, 2 of 2)

- [On Grid Graph Reachability and Puzzle Games](https://mlsanity.com/paper/2310.01378/) (2023)
- [A Good Snowman is Hard to Plan](https://mlsanity.com/paper/2310.01471/) (2023)

## Abstract (arXiv)

We define the concept of a monotonic theory and show how to build efficient SMT (SAT Modulo Theory) solvers, including effective theory propagation and clause learning, for such theories. We present examples showing that monotonic theories arise from many common problems, e.g., graph properties such as reachability, shortest paths, connected components, minimum spanning tree, and max-flow/min-cut, and then demonstrate our framework by building SMT solvers for each of these theories. We apply these solvers to procedural content generation problems, demonstrating major speed-ups over state-of-the-art approaches based on SAT or Answer Set Programming, and easily solving several instances that were previously impractical to solve.