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JaouaMilietal91

1. A Jaoua & A Mili & N Boudriga & J L Durieux
2. Regularity of Relations: A Measure of Uniformity
3. Theoretical Comp Sci. V79n2(Feb 1991)pp323-339
4. CR904-0236
5. See Milietal89

1. |-for all R:@(X,Y), R==>R;/R;R.
2. Regular::={R || R;/R;R==> R}.
3. (-2, -1)|-Regular = {R || R;/R;R=R}.
4. kernel(R)::= {}<>s'.R==>s.R,
5. (kernel)|-kernel(R) in reflexive & transitive.
6. nucleus(R)::=R;/R,
7. (-1)|-nucleus(R) in reflexive & symmetric. (?????)
8. (Regular)|-If equivalence(R)then R in Regular.
9. (Regular)|-post(R)>=={u.R||u:pre(R)} iff Regular.
10. (Regular, nucleus, kernal)|-If Regular R then nucleus(R) = kernel(R) in reflexive & symmetric & transitive.
11. |-form(x'=f(x,...)) is regular. ...
12. |-For all Regular R, Functions f, f;R in Regular.
13. Rational::={R||for some X, f,g :dom(R)->X(R=f;/g)}.
14. |-Regular iff Rational. For all R, some f,g, R=/f;g.

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