Definition:P-Closure of Relation
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Definition
Let $\RR = \struct {S, T, R}$ be a relation on the sets $S$ and $T$:
- $R \subseteq S \times T$
Let $P$ be a property of relations.
Let $\RR' = \struct {S, T, R'}$ be the relation on $S \times T$ such that:
- $R \subseteq R'$
- $\RR'$ is the smallest relation on $S \times T$ with respect to the subset ordering on $S \times T$
- $R'$ has the property $P$.
Then $\RR'$ is known as the $P$-closure of $\RR$.
Sources
- 1979: John E. Hopcroft and Jeffrey D. Ullman: Introduction to Automata Theory, Languages, and Computation ... (previous) ... (next): Chapter $1$: Preliminaries: $1.5$ Relations: Closures of Relations