Deciding FO-rewritability of regular languages and ontology-mediated queries in Linear Temporal Logic Article Swipe
YOU?
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· 2022
· Open Access
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· DOI: https://doi.org/10.48550/arxiv.2207.06210
Our concern is the problem of determining the data complexity of answering an ontology-mediated query (OMQ) formulated in linear temporal logic LTL over (Z,<) and deciding whether it is rewritable to an FO(<)-query, possibly with some extra predicates. First, we observe that, in line with the circuit complexity and FO-definability of regular languages, OMQ answering in AC^0, ACC^0 and NC^1 coincides with FO(<,\equiv)-rewritability using unary predicates x \equiv 0 (mod n), FO(<,MOD)-rewritability, and FO(RPR)-rewritability using relational primitive recursion, respectively. We prove that, similarly to known PSPACE-completeness of recognising FO(<)-definability of regular languages, deciding FO(<,\equiv)- and FO(<,MOD)-definability is also \PSPACE-complete (unless ACC^0 = NC^1). We then use this result to show that deciding FO(<)-, FO(<,\equiv)- and FO(<,MOD)-rewritability of LTL OMQs is EXPSPACE-complete, and that these problems become PSPACE-complete for OMQs with a linear Horn ontology and an atomic query, and also a positive query in the cases of FO(<)- and FO(<,\equiv)-rewritability. Further, we consider FO(<)-rewritability of OMQs with a binary-clause ontology and identify OMQ classes, for which deciding it is PSPACE-, Pi_2^p- and coNP-complete.
Related Topics
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2207.06210
- https://arxiv.org/pdf/2207.06210
- OA Status
- green
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4285483635
Raw OpenAlex JSON
- OpenAlex ID
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https://openalex.org/W4285483635Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.48550/arxiv.2207.06210Digital Object Identifier
- Title
-
Deciding FO-rewritability of regular languages and ontology-mediated queries in Linear Temporal LogicWork title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
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2022Year of publication
- Publication date
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2022-07-13Full publication date if available
- Authors
-
Agi Kurucz, Vladislav Ryzhikov, Yury Savateev, Michael ZakharyaschevList of authors in order
- Landing page
-
https://arxiv.org/abs/2207.06210Publisher landing page
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https://arxiv.org/pdf/2207.06210Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
-
https://arxiv.org/pdf/2207.06210Direct OA link when available
- Concepts
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Unary operation, PSPACE, Mathematics, P, Time complexity, Discrete mathematics, Decidability, Temporal logic, Linear temporal logic, Combinatorics, Theoretical computer science, Computational complexity theory, Computer science, AlgorithmTop concepts (fields/topics) attached by OpenAlex
- Cited by
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0Total citation count in OpenAlex
- Related works (count)
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10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.FO(<)-rewritability | 153 |
| abstract_inverted_index.FO(<,MOD)-definability | 95 |
| abstract_inverted_index.FO(<,MOD)-rewritability | 115 |
| abstract_inverted_index.FO(<,MOD)-rewritability, | 71 |
| abstract_inverted_index.FO(<,\equiv)-rewritability | 62 |
| abstract_inverted_index.FO(<,\equiv)-rewritability. | 149 |
| cited_by_percentile_year | |
| countries_distinct_count | 0 |
| institutions_distinct_count | 4 |
| sustainable_development_goals[0].id | https://metadata.un.org/sdg/4 |
| sustainable_development_goals[0].score | 0.4099999964237213 |
| sustainable_development_goals[0].display_name | Quality Education |
| citation_normalized_percentile.value | 0.08857149 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | False |