# Reachability analysis of first-order definable pushdown systems

arXiv: https://arxiv.org/abs/1504.02651 · HTML: https://mlsanity.com/paper/1504.02651/

## Key facts

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

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

- [Solvability of orbit-finite systems of linear equations](https://mlsanity.com/paper/2201.09060/) (2022)

## Abstract (arXiv)

We study pushdown systems where control states, stack alphabet, and transition relation, instead of being finite, are first-order definable in a fixed countably-infinite structure. We show that the reachability analysis can be addressed with the well-known saturation technique for the wide class of oligomorphic structures. Moreover, for the more restrictive homogeneous structures, we are able to give concrete complexity upper bounds. We show ample applicability of our technique by presenting several concrete examples of homogeneous structures, subsuming, with optimal complexity, known results from the literature. We show that infinitely many such examples of homogeneous structures can be obtained with the classical wreath product construction.