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Bernoulli variable algebra

I have been working on a Mathematica package used to predict the reliability of
complex redundent systems. The calculations, which are done symboliclly, become
quite complex. Since all of the variables used are Bernoulli variables, i.e.
take on only values of 0 or 1, the expressions must be simplified by use of the
rule x_^n_->x. My problem is this, the expressions are complex and large and,
as a result the Mathematica Kernal runs out of memory trying to expand the
expressions. I know, from other techniques, that the resulting expressions
after application of the  x_^n_->x rule are still large (> 1000 terms) they are
not unmanageable. (The expressions prior to applying the rule might be on the
order of 10^6 terms) If a technique could be devised for accomplishing the
effect of the above transformation without first requiring the full expansion
of the expressions it would be possible to greatly simplify the required
analysis. Is anyone aware of a technique for the simplification of algebraic
expressions of Bernoulli variables without requiring expansion of the
expression first?

Any hints would be greatly appreciated.
Al Myers

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