Precision on demand: an improvement in probabilistic hashing

In explicit state (enumerative) model checking, state vectors are often represented in a compressed form in order to reduce storage needs, typically employing fingerprints, bithashes, or state signatures. When using this kind of techniques, it could happen that the compressed image of a nonvisited state s matches that of a visited state s0 6= s, thus s and potentially many of its descendants are omitted from search. If any of these omitted states was an error state, we could also have false positives. We present a new technique which reduces the number of omitted states, by requiring a slightly higher computation time, but without employing any additional memory. Our technique works for depth-first search based state exploration, and exploits the fact that when a non-terminal state t is represented in the hash table, then one of the successors of t (the first to be expanded next, typically the left-most) is also represented in the visited states hash table. Therefore, instead of backing off when the compressed state images match, our algorithm persists to see if any of the left-most successors also matches (the number of successors which are considered for each state is user-defined, thus we name our approach Precision on Demand or POD).