We show that the satisfiability problem for the quantifier-free theory of product structures with the equicardinality relation is in NP. As an application, we extend the combinatory array logic fragment to handle cardinality constraints. The resulting fragment is independent of the base element and index set theories.

中文翻译：

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数组作为幂的 NP 可满足性

我们证明了具有等基数关系的产品结构的无量词理论的可满足性问题在 NP 中。作为一个应用程序，我们扩展了组合数组逻辑片段来处理基数约束。结果片段独立于基本元素和索引集理论。