Many test generation algorithms use unique input/output sequences (UIOs) that identify states of the finite state machine specification M. However, it is known that UIO checking the existence of UIO sequences is PSPACE-complete. As a result, some UIO generation algorithms utilise what are called invertible sequences; these allow one to construct additional UIOs once a UIO has been found. We consider three optimisation problems associated with invertible sequences: deciding whether there is a (proper) invertible sequence of length at least K; deciding whether there is a set of invertible sequences for state set S′ that contains at most K input sequences; and deciding whether there is a single input sequence that defines invertible sequences that take state set S″ to state set S′. We prove that the first two problems are NP-complete and the third is PSPACE-complete. These results imply that we should investigate heuristics for these problems.
CITATION STYLE
Hierons, R. M., Mousavi, M. R., Thomsen, M. K., & Türker, U. C. (2017). Hardness of deriving invertible sequences from finite state machines. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 10139 LNCS, pp. 147–160). Springer Verlag. https://doi.org/10.1007/978-3-319-51963-0_12
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