# Semantic Tree-Width and Path-Width of Conjunctive Regular Path Queries

arXiv: https://arxiv.org/abs/2212.01679 · HTML: https://mlsanity.com/paper/2212.01679/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Dec 2022.

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

- [A Logical View of GNN-Style Computation and the Role of Activation Functions](https://mlsanity.com/paper/2512.19332/) (2025)

## Abstract (arXiv)

We show that the problem of whether a query is equivalent to a query of tree-width k is decidable, for the class of Unions of Conjunctive Regular Path Queries with two-way navigation (UC2RPQs). A previous result by Barcel'o, Romero, and Vardi [SIAM Journal on Computing, 2016] has shown decidability for the case k=1, and here we extend this result showing that decidability in fact holds for any arbitrary k≥ 1. The algorithm is in 2ExpSpace, but for the restricted but practically relevant case where all regular expressions of the query are of the form a^* or (a1 + dotsb + an) we show that the complexity of the problem drops to PiP2. We also investigate the related problem of approximating a UC2RPQ by queries of small tree-width. We exhibit an algorithm which, for any fixed number k, builds the maximal under-approximation of tree-width k of a UC2RPQ. The maximal under-approximation of tree-width k of a query q is a query q' of tree-width k which is contained in q in a maximal and unique way, that is, such that for every query q'' of tree-width k, if q'' is contained in q then q'' is also contained in q'. Our approach is shown to be robust, in the sense that it allows also to test equivalence with queries of a given path-width, it also covers the previously known result for k=1, and it allows to test for equivalence of whether a (one-way) UCRPQ is equivalent to a UCRPQ of a given tree-width (or path-width).