On the Decidability of Semi-Linearity for Semi-Algebraic Sets and its Implications for Spatial Databases (extended abstract)
Summary: Proves decidability of whether a semi-algebraic set is semi-linear, highlights the role of coefficient types and the geometric notion of regularity, and shows regular points are computable in FO+linear. Consequence: yields a syntactic language exactly capturing the FO+poly queries that are linear, circumventing previous undecidability of testing linearity. (summarized by gpt-5-mini on Feb 09 2026)
Incoming Non-self Citations Over Time
Authors
- 1. Freddy Dumortier (University of Limburg)
- 2. Marc Gyssens (University of Limburg)
- 3. Luc Vandeurzen (University of Limburg)
- 4. Dirk Van Gucht (Indiana University)
BibTeX Citation
@inproceedings{dumortier_pods97,
address = {New York, NY, USA},
series = {{PODS} '97},
title = {{On the Decidability of Semi-Linearity for Semi-Algebraic Sets and its Implications for Spatial Databases (extended abstract)}},
url = {https://dl.acm.org/doi/10.1145/263661.263670},
doi = {10.1145/263661.263670},
booktitle = {Proceedings of the {ACM} {SIGMOD} Symposium on {Principles} of {Database} {Systems}},
publisher = {Association for Computing Machinery},
author = {Dumortier, Freddy and Gyssens, Marc and Vandeurzen, Luc and Van Gucht, Dirk},
year = {1997}
}
Incoming Citations (Sorted by Pagerank)
Showing 6 of 6 citing papers.
| Rank | Citing Paper | Year | Venue | Pagerank |
|---|---|---|---|---|
| 1,589 | Efficient Searching with Linear Constraints (Extended Abstract) | 1998 | PODS | 0.00010139591 |
| 3,099 | The DEDALE System for Complex Spatial Queries | 1998 | SIGMOD | 7.6508573e-05 |
| 4,292 | An Expressive Language for Linear Spatial Database Queries (extended abstract) | 1998 | PODS | 6.6820595e-05 |
| 4,317 | Safe Constraint Queries | 1998 | PODS | 6.6681018e-05 |
| 13,165 | Fixed-Point Query Languages for Linear Constraint Databases | 2000 | PODS | 4.9793485e-05 |
| 13,166 | Linear approximation of planar spatial databases using transitive-closure logic | 2000 | PODS | 4.9793485e-05 |
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Outgoing Citations (Sorted by Pagerank)
Showing 4 of 4 cited papers.
Citations counted here include only citations to other VLDB/SIGMOD/CIDR/PODS papers in this database.
| Rank | Cited Paper | Year | Venue | Pagerank |
|---|---|---|---|---|
| 914 | Constraint Programming and Database Languages: A Tutorial | 1995 | PODS | 0.00013104061 |
| 1,512 | Towards a Theory of Spatial Database Queries (Extended Abstract) | 1994 | PODS | 0.00010429539 |
| 1,950 | Relational Expressive Power of Constraint Query Languages | 1996 | PODS | 9.3195393e-05 |
| 3,667 | The LyriC Language: Querying Constraint Objects | 1995 | SIGMOD | 7.1163605e-05 |
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