Minimization of Counterexamples in SPIN

Abstract

Abstract. We propose an algorithm to find a counterexample to some property in a finite state program. This algorithm is derived from SPIN's one, but it finds a counterexample faster than SPIN does. In particular it still works in linear time. Compared with SPIN's algorithm, it requires only one additional bit per state stored. We further propose another algorithm to compute a counterexample of minimal size. Again, this algorithm does not use more memory than SPIN does to approximate a minimal counterexample. The cost to find a counterexample of minimal size is that one has to revisit more states than SPIN. We provide an implementation and discuss experimental results.

Larger Automata and Less Work for LTL Model Checking

“…Subsequent improvements [15,19,22,27] has not only made it compatible with partial-order methods, but has also led to a significant reduction in the number of states and transitions it needs to explore. The core algorithm has also been adapted for use with generalized Büchi automata [32] and heuristic search [2,11].…”

Shortest Counterexamples for Symbolic Model Checking of LTL with Past

“…It does not find shortest counterexamples. Gastin et al propose an algorithm [11] to minimize the length of counterexamples, which may visit a state an exponential number of times.…”

Minimal Counterexamples in O(n log n) Memory and O(n^2) Time

“…We compared two algorithms: our algorithm, which we call "3B" and a depth-first-based search introduced in [6], which we call "GMZ". We recorded the number of transitions explored every time an algorithm improved the shortest found counterexample to measure the rate of convergence.…”

“…It is widely thought that finding minimal counterexamples in polynomial time requires the shortest paths from all states to all states, storing a quadratic amount of information [6]. We show that O(n log n) memory suffices.…”

“…Minimal counterexamples in explicit state spaces have recently been studied in [6], where a depth-first search (DFS) is applied in a novel fashion. Heuristic approaches to short counterexamples have been studied in [12] and, in combination with partial order reductions, in [5].…”