{"title":"Tractable Combinations of Temporal CSPs","authors":"M. Bodirsky, Johannes Greiner, Jakub Rydval","doi":"10.46298/lmcs-18(2:11)2022","DOIUrl":null,"url":null,"abstract":"The constraint satisfaction problem (CSP) of a first-order theory $T$ is the computational problem of deciding whether a given conjunction of atomic formulas is satisfiable in some model of $T$. We study the computational complexity of $\\mathrm{CSP}(T_1 \\cup T_2)$ where $T_1$ and $T_2$ are theories with disjoint finite relational signatures. We prove that if $T_1$ and $T_2$ are the theories of temporal structures, i.e., structures where all relations have a first-order definition in $(\\mathbb{Q};<)$, then $\\mathrm{CSP}(T_1 \\cup T_2)$ is in P or NP-complete. To this end we prove a purely algebraic statement about the structure of the lattice of locally closed clones over the domain ${\\mathbb Q}$ that contain $\\mathrm{Aut}(\\mathbb{Q};<)$.","PeriodicalId":314387,"journal":{"name":"Log. Methods Comput. Sci.","volume":"3 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2020-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Log. Methods Comput. Sci.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.46298/lmcs-18(2:11)2022","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
Abstract
The constraint satisfaction problem (CSP) of a first-order theory $T$ is the computational problem of deciding whether a given conjunction of atomic formulas is satisfiable in some model of $T$. We study the computational complexity of $\mathrm{CSP}(T_1 \cup T_2)$ where $T_1$ and $T_2$ are theories with disjoint finite relational signatures. We prove that if $T_1$ and $T_2$ are the theories of temporal structures, i.e., structures where all relations have a first-order definition in $(\mathbb{Q};<)$, then $\mathrm{CSP}(T_1 \cup T_2)$ is in P or NP-complete. To this end we prove a purely algebraic statement about the structure of the lattice of locally closed clones over the domain ${\mathbb Q}$ that contain $\mathrm{Aut}(\mathbb{Q};<)$.