Aside from WF and SF?

[Chris Ortiz]

Hello,

WF_v(A) == []([]ENABLED <<A>>_v => <><<A>>_v) and

SF_v(A) == []([]<>ENABLED <<A>>_v => <><<A>>_v)

Is there

[]( ENABLED <<A>>_v => <><<A>>_v) and

[](<>[]ENABLED <<A>>_v => <><<A>>_v ?

And what could they mean?

Thanks and best regards,

Chris (Zitro)

[Andrew Helwer]

[](ENABLED <<A>>_v => <><<A>>_v) is equivalent to []((ENABLED A) ~> <><<A>>_v) which means if an A step is enabled (like at all), eventually it will be taken; moreover, it will also be taken after every time an A step is enabled in the future. This is like an even stronger fairness assumption, but looking through the texts I have it does not seem to be a standard one. The usual next strongest fairness assumption in temporal logic is unconditional fairness, which is just []<><<A>>_v. There are a lot of fairness definitions out there though so I'm sure someone has covered & named it.

For the second one, since P => <>P, it seems to be implied by weak fairness. So it is at most as strong as weak fairness. Is it any weaker than weak fairness? I can't think of how it could be, but then we should be able to rewrite it into weak fairness. And there I am somewhat at a loss.

Andrew

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