## Quick Reference

Of a transitive binary relation *R*. A relation *R*✻ defined as follows: *x R*✻ *y* iff there exists a sequence *x*=*x*_{0},*x*_{1},…, *x** _{n}*=

*y*such that

*n*> 0 and

*x*

_{i}*R*x

_{i}_{+1},

*i*=0,1,2,…,

*n*-1 It follows from the transitivity property that if

*x R y*then

*x R*✻

*y*and that

*R*is a subset of

*R*✻.

*x R*✻ *y*

*x*=*x*_{0},*x*_{1},…, *x** _{n}*=

*y*

*x*_{i}*R* x_{i}_{+1}, *i*=0,1,2,…, *n*-1

if *x R y* then *x R*✻ *y*

Reflexive closure is similar to transitive closure but includes the possibility that *n* = 0. Transitive and reflexive closures play important roles in parsing and compiling techniques and in finding paths in graphs.

*Subjects:*
Computing.

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