Preimage problems for deterministic finite automata

Berlinkov, Mikhail V.; Ferens, Robert; Szykuła, Marek

doi:10.1016/j.jcss.2020.08.002

Cited by 7 publications

(11 citation statements)

References 27 publications

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“…Furthermore, we investigate two problems related to subset synchronization, namely the problem if we can map the whole state set into a given target set by some word, and if we can map any given starting set into another target set. Both problems are PSPACE-complete in general [2,3,17,21,25,28]. However, for weakly acyclic automata the former becomes polynomial time solvable, as we will show here, and the latter becomes NP-complete.…”

Section: Introductionmentioning

confidence: 69%

“…Here, we will investigate the followig problems from [2,3,17,21,25,28,31] for weakly acyclic input automata. Definition 9.…”

Section: Subset Synchronization Problemsmentioning

confidence: 99%

“…This notion has a wide range of applications, from software testing, circuit synthesis, communication engineering and the like, see [28,30]. The famous Černý conjecture [7] states that a minimal length synchronizing word, for an n-state automaton, has length at most pn ´1q 2 . We refer to the mentioned survey articles [28,30] for details 1 .…”

Section: Introductionmentioning

confidence: 99%

“…Related synchronization problems for weakly acyclic automata were previously investigated in [27]. For example, in [27], it was shown that the problem to decide if a given subset of states could be mapped to a single state, a problem PSPACE-complete for general automata [2,25], is NP-complete for weakly acyclic automata.…”

Section: Introductionmentioning

confidence: 99%

“…Similar subset synchronization problems, for general, strongly connected and synchronizing automata, were investigated in [2].…”

Section: Introductionmentioning

confidence: 99%

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Constrained Synchronization and Subset Synchronization Problems for Weakly Acyclic Automata

Hoffmann¹

2021

Preprint

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We investigate the constrained synchronization problem for weakly acyclic, or partially ordered, input automata. We show that, for input automata of this type, the problem is always in NP. Furthermore, we give a full classification of the realizable complexities for constraint automata with at most two states and over a ternary alphabet. We find that most constrained problems that are PSPACE-complete in general become NP-complete. However, there also exist constrained problems that are PSPACE-complete in the general setting but become polynomial time solvable when considered for weakly acyclic input automata. We also investigate two problems related to subset synchronization, namely if there exists a word mapping all states into a given target subset of states, and if there exists a word mapping one subset into another. Both problems are PSPACE-complete in general, but in our setting the former is polynomial time solvable and the latter is NP-complete.

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