# Faster Possibility Detection by Combining Two Approaches

## Abstract:

A new algorithm is presented for detecting whether a particular
computation of an asynchronous distributed system satisfies $\Poss\Phi$
(read ``possibly $\Phi$''), meaning the system could have passed through
a global state satisfying $\Phi$. Like the algorithm of Cooper and
Marzullo, $\Phi$ may be any global state predicate; and like the
algorithm of Garg and Waldecker, $\Poss\Phi$ is detected quite
efficiently if $\Phi$ has a certain structure. The new algorithm
exploits the structure of some predicates $\Phi$ not handled by Garg and
Waldecker's algorithm to detect $\Poss\Phi$ more efficiently than is
possible with any algorithm that, like Cooper and Marzullo's, evaluates
$\Phi$ on every global state through which the system could have passed.
A second algorithm is also presented for off-line detection of
$\Poss\Phi$. It uses Strassen's scheme for fast matrix multiplication.
The intrinsic complexity of off-line and on-line detection of
$\Poss\Phi$ is discussed.

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