A family of sets has the equal union property if there exist two nonempty disjoint subfamilies having equal unions and has the full equal union property if, in addition, all sets are included. Both recognition problems are NP-complete even when ...
This paper is motivated by the open question whether the union of two disjoint NP-complete sets always is NP-complete. We discover that such unions retain much of the complexity of their single components. More precisely, they are complete with respect ...
Let $A$ be a language and $C$ be a class of languages. $A$ is said to be s-C-close (s-C-outside-close) if there exists $B \in C$ such that $\parallel (A \bigtriangleup B)^{\leq n}\parallel \leq s(n)$ (and $A \subseteq B $). If $A$ is q-C-close (q-C-...
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