Cheap and Small Counterexamples

Minimal counterexamples are desirable, but expensive to compute. We propose four algorithms for computing small counterexamples that approximate the shortest case. Three of these use a new algorithm for automata-theoretic linear-time model checking, based on an early algorithm by Dijkstra for detecting strongly connected components. All four of the approximation algorithms rely on transitions shuffling; we show that the default transition ordering can behave badly. The algorithms are compared to a standard shortest counterexample algorithm on a large public data set.