  Identifying a temporal pattern of events is a fundamental task of on-line
(real-time) verification. We present efficient schemes for on-line monitoring
of events for identifying desired/undesired patterns of events. The schemes use
preprocessing to ensure that the number of comparisons during run-time is
minimized. In particular, the first comparison following the time point when an
execution sub-sequence cannot be further extended to satisfy the temporal
requirements, halts the process that monitors the sub-sequence.
