Definition:Reflexive Transitive Closure/Reflexive Closure of Transitive Closure
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Definition
Let $\RR$ be a relation on a set $S$.
The reflexive transitive closure of $\RR$ is denoted $\RR^*$, and is defined as the reflexive closure of the transitive closure of $\RR$:
- $\RR^* = \paren {\RR^+}^=$
Also see
- Results about reflexive transitive closures can be found here.
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