RE: [sv-ac] some thoughts on non-vacuity

Hi John,

I think I like your definitions. They are not that intuitive but they
will not produce false negatives (as far as I can see) and if a property
never pass non-vacuously, that probably because of a problem.

Doron 

>>-----Original Message-----
>>From: owner-sv-ac@server.eda.org [mailto:owner-sv-ac@server.eda.org]
On
>>Behalf Of John Havlicek
>>Sent: Monday, January 14, 2008 8:18 PM
>>To: Bustan, Doron
>>Cc: john.havlicek@freescale.com; sv-ac@server.eda.org
>>Subject: Re: [sv-ac] some thoughts on non-vacuity
>>
>>Hi Doron:
>>
>>You are right, I put them backwards!  I should have put
>>
>>   vacuous_true  = 0 |-> 0
>>   vacuous_false = not(vacuous_true)
>>
>>It's not so important exactly how these are defined as long as
>>you the following holds:
>>
>>   For w a non-empty natural word (i.e., no letter of w is \top or
\bot),
>>
>>      w |/= vacuous_false and w |/=^{non} vacuous_false
>>      w |=  vacuous_true  and w |/=^{non} vacuous_true
>>
>>J.H.
>>
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>>> Thread-Topic: [sv-ac] some thoughts on non-vacuity
>>> thread-index: AchWt3onFqvX8IhASJS/fxfqXlHxTAAB+uLQ
>>> From: "Bustan, Doron" <doron.bustan@intel.com>
>>> Cc: <sv-ac@eda.org>
>>> X-OriginalArrivalTime: 14 Jan 2008 15:10:45.0900 (UTC)
>>FILETIME=[A3541CC0:01C856BF]
>>>
>>> Hi John,
>>>
>>> I don't understand why
>>>
>>> >>
>>> >>  vacuous_false =3D 0 |-> 0.
>>> >>  vacuous_true =3D not(vacuous_false)
>>> >>
>>> >>Assume that w is a non-empty natural word (i.e., no letter of w is
>>> \top or
>>> >>\bot).
>>> >>Then
>>> >>
>>> >>  w |/=3D vacuous_false and w |/=3D^{non} vacuous_false
>>> >>  w |=3D  vacuous_true  and w |/=3D^{non} vacuous_true
>>> >>
>>> >>
>>>
>>> Isn't 0 |-> 0 a tautology?=20
>>>
>>> Doron
>>
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