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 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 $(Q;<)$, then 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 $Q$ that contain Aut$(Q;<)$.
翻译:一阶理论T的制约满意度问题(CSP)是计算问题,即确定原子公式的某一组合是否在T.的某种模型中可以对准。我们研究了CSP$(T_1\cup T_2)的计算复杂性,其中1美元和2美元是带有不连接的有限关系签名的理论。我们证明,如果1美元和2美元是时间结构理论,即所有关系均以美元(Q; < $)确定一级定义的结构,然后是CSP$(T_1\cup T_2)是P或NP的计算复杂性。为此,我们证明,关于域内含有Aut$(Q; < 美元)的本地封闭克隆的阵列结构的纯代数说明。