Boots – shoes – and leggings
Patent
1996-11-01
1998-04-07
Voeltz, Emanuel T.
Boots, shoes, and leggings
364550, 36455101, 395 24, 395 51, G06F 1100
Patent
active
057372420
DESCRIPTION:
BRIEF SUMMARY
FIELD OF THE INVENTION
The invention relates to a method for automatically determining the probabilities associated with a Boolean function, with the aid of a data processing machine.
BACKGROUND OF THE INVENTION
Boolean functions are manipulated in many fields. By way of example, synthesis and optimization of electronic circuits and system fault analysis can employ the manipulation of Boolean functions.
In fault analysis, for example, the occurrence of a fault as a function of external events capable of causing this fault can be analyzed with the aid of a Boolean function.
More generally, in any system, the occurrence of a reference event or of an action, when it is a function of one or more concomitant events, also called microscopic events, can thus be analyzed. Each microscopic event is accordingly a variable of the function.
For comprehension of the ensuing description, it is appropriate to recall some concepts and definitions relating to Boolean functions, and the terminology used.
Let us assume a Boolean function f is defined by the following formula: f=x.sub.1 x.sub.2 *+x.sub.1 *x.sub.2 x.sub.3. This is said to be a propositional formula, and x.sub.1, x.sub.2, x.sub.3 are propositional variables, corresponding to atomic events capable of causing the appearance of the reference event symbolized by the letter f and represented by the formula.
Hence in the analysis of system faults the atomic events are the fault causes, and the reference event is a particular fault associated with these causes combined with one another in certain ways.
The terms "x.sub.1 ", "x.sub.2 " "x.sub.3 " and "x.sub.1 *" "x.sub.2 *" "x.sub.3 *", which appear in the formula, are literals corresponding to the propositional variables x.sub.1, x.sub.2, x.sub.3. A literal shows how the propositional variable is involved in the function, or in other words whether the occurrence or nonoccurrence of the associated event is decisive or unimportant. x.sub.1 x.sub.2 * and x.sub.1 * x.sub.2 x.sub.3 are products of literals. A product is accordingly a conjunction of variables and negations of variables.
The first product, x.sub.1 x2*, means that the presence or absence of the third variable x.sub.3 is unimportant.
The formula means that the reference event occurs (f=1) when simultaneously the first atomic event x.sub.1 occurs (x.sub.1 =1) and the second event x.sub.2 does not occur (x.sub.2 =0), or when simultaneously the first event x.sub.1 does not occur and the second and third events x.sub.2 and x.sub.3 do occur.
Such a formula is in fact the result of either simulation or analysis done with a prototype.
In analysis of a system (in terms of function or for faults), such a formula is conventionally shown in the form of a table that shows the various products of the function. The table associated with the function given in this example would accordingly contain the products x.sub.1 x.sub.2 * and x.sub.1 * x.sub.2 x.sub.3.
In the field of system fault analysis, a table of this kind is called a fault tree. More generally, it may be called an event tree.
Such a tree may be used to perform various analyses or calculations relating to the behavior of the system. In particular, one may contemplate calculating the probability of occurrence of a reference event as a function of that of each of the atomic events.
To that end, the table shows not only the products contributing to the occurrence of the function but also the probability of occurrence of each atomic event. This probability has been determined, for instance during simulation or analysis.
Nevertheless, calculating the probability of each reference event, such as a fault, must be done after that analysis or simulation. This calculation needs to be automated, because either the table includes an extremely large number of products, or a large number of reference events must be analyzed.
Methods known thus far do not provide satisfaction. In fact, they begin with approximation formulas that require calculation of the implicants of the function.
It will be recalled that an implicant of a
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Coudert Olivier
Madre Jean-Christophe
Bull S.A.
Kondracki Edward J.
Voeltz Emanuel T.
Wachsman Hal D.
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