Hardness of deriving invertible sequences from finite state machines

TY - GEN

T1 - Hardness of deriving invertible sequences from finite state machines

AU - Hierons, Robert M.

AU - Mousavi, Mohammad Reza

AU - Thomsen, Michael Kirkedal

AU - Türker, Uraz Cengiz

N1 - Conference code: 43

PY - 2017

Y1 - 2017

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85010657662&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-51963-0_12

DO - 10.1007/978-3-319-51963-0_12

M3 - Article in proceedings

AN - SCOPUS:85010657662

SN - 978-3-319-51962-3

T3 - Lecture notes in computer science

SP - 147

EP - 160

BT - SOFSEM 2017: Theory and Practice of Computer Science

A2 - Steffen, Bernhard

A2 - Baier, Christel

A2 - van den Brand, Mark

A2 - Eder, Johann

A2 - Hinchey, Mike

A2 - Margaria, Tiziana

PB - Springer

T2 - 43rd International Conference on Current Trends in Theory and Practice of Computer Science

Y2 - 16 January 2017 through 20 January 2017

ER -