$Π_{2}^{P}$ vs PSpace Dichotomy for the Quantified Constraint Satisfaction Problem
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929550686945280 |
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| author | Zhuk, Dmitriy |
| author_facet | Zhuk, Dmitriy |
| contents | The Quantified Constraint Satisfaction Problem is the problem of evaluating a sentence with both quantifiers, over relations from some constraint language, with conjunction as the only connective. We show that for any constraint language on a finite domain the Quantified Constraint Satisfaction Problem is either in $Π_{2}^{P}$, or PSpace-complete. Additionally, we build a constraint language on a 6-element domain such that the Quantified Constraint Satisfaction Problem over this language is $Π_{2}^{P}$-complete. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_03844 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $Π_{2}^{P}$ vs PSpace Dichotomy for the Quantified Constraint Satisfaction Problem Zhuk, Dmitriy Computational Complexity Logic in Computer Science Logic The Quantified Constraint Satisfaction Problem is the problem of evaluating a sentence with both quantifiers, over relations from some constraint language, with conjunction as the only connective. We show that for any constraint language on a finite domain the Quantified Constraint Satisfaction Problem is either in $Π_{2}^{P}$, or PSpace-complete. Additionally, we build a constraint language on a 6-element domain such that the Quantified Constraint Satisfaction Problem over this language is $Π_{2}^{P}$-complete. |
| title | $Π_{2}^{P}$ vs PSpace Dichotomy for the Quantified Constraint Satisfaction Problem |
| topic | Computational Complexity Logic in Computer Science Logic |
| url | https://arxiv.org/abs/2404.03844 |