Languages Generated by Conjunctive Query Fragments of FC[REG

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$$\textsf{FC}$$ is a finite-model variant on the theory of concatenation, $$\textsf{FC}[\textsf{REG}]$$ extends $$\textsf{FC}$$ with regular constraints. This paper considers the languages generated by their conjunctive query fragments, $$\mathsf {FC \hbox {-} CQ}$$ and $$\mathsf {FC[REG] \hbox {-} CQ}$$ . We compare the expressive power of $$\mathsf {FC[REG] \hbox {-} CQ}$$ to that of various related language generators, such as regular expressions, patterns, and typed patterns. We then consider decision problems for $$\mathsf {FC \hbox {-} CQ}$$ and $$\mathsf {FC[REG] \hbox {-} CQ}$$ , and show that certain static analysis problems (such as equivalence and regularity) are undecidable. While this paper defines $$\mathsf {FC \hbox {-} CQ}$$ based on the logic $$\textsf{FC}$$ , they can equally be understood as synchronized intersections of pattern languages, or as systems of restricted word equations.