Better Bounds for Event Sequencing Testing

A permutation of a sequence of events is a common construction in many testing environments. Covering all possible permutations has clearly an exponential behavior; so one can ask for partial (easier) requirement, to cover all possible orders: permutations induced on of a small cardinality subset of elements. In our paper we show better (both lower and upper) bounds on this event sequencing testing problem. We also discuss another variant of the problem where we impose restrictions on the permutations. In this case we show how to achieve an exponential growth in the complexity of the problem. We also give solutions for specific cases of the problem.