Computational Complexity of Synchronization Under Regular Commutative Constraints

Hoffmann, Stefan

doi:10.1007/978-3-030-58150-3_37

Cited by 7 publications

(4 citation statements)

References 41 publications

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“…Acknowledgement. I thank anonymous reviewers of the extended version (submitted) of [27], whose feedback influenced Section 3. I am also grateful to the reviewers of a previous version.…”

Section: S Hoffmannmentioning

confidence: 99%

Constrained Synchronization for Commutative Automata and Automata with Simple Idempotents

Hoffmann

2021

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For general input automata, there exist regular constraint languages such that asking if a given input automaton admits a synchronizing word in the constraint language is PSPACE-complete or NP-complete. Here, we investigate this problem for commutative automata over an arbitrary alphabet and automata with simple idempotents over a binary alphabet as input automata. The latter class contains, for example, the Černý family of automata. We find that for commutative input automata, the problem is always solvable in polynomial time, for every constraint language. For input automata with simple idempotents over a binary alphabet and with a constraint language given by a partial automaton with up to three states, the constrained synchronization problem is also solvable in polynomial time.

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“…Acknowledgement. I thank anonymous reviewers of the extended version (submitted) of [27], whose feedback influenced Section 3. I am also grateful to the reviewers of a previous version.…”

Section: S Hoffmannmentioning

confidence: 99%

Constrained Synchronization for Commutative Automata and Automata with Simple Idempotents

Hoffmann

2021

Preprint

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“…It is natural to extend this result to other language classes, or even to give a complete classification of all the complexity classes that could arise. For commutative regular constraint languages, a full classification of the realizable complexities was given in [16]. In [17], it was shown that for polycyclic constraint languages, the problem is always in NP.…”

Section: Introductionmentioning

confidence: 99%

Constrained Synchronization and Subset Synchronization Problems for Weakly Acyclic Automata

Hoffmann¹

2021

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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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“…In [12] the result for two-state automata was generalized to arbitrary alphabets, and a complexity classification for special three-state constraint automata over a binary alphabet was given. As shown in [11], for regular commutative constraint languages, we only find constraint problems that are NP-complete, PSPACE-complete, or solvable in polynomial time. In all the mentioned work [8,11,12], it was noted that the constraint automata for which the corresponding constraint synchronization problem is NP-complete admit a special form, which we generalize in this work.…”

Section: Introductionmentioning

confidence: 99%

“…As shown in [11], for regular commutative constraint languages, we only find constraint problems that are NP-complete, PSPACE-complete, or solvable in polynomial time. In all the mentioned work [8,11,12], it was noted that the constraint automata for which the corresponding constraint synchronization problem is NP-complete admit a special form, which we generalize in this work.…”

Section: Introductionmentioning

confidence: 99%

On a Class of Constrained Synchronization Problems in NP

Hoffmann

2020

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The class of known constraint automata for which the constrained synchronization problem is in NP all admit a special form. In this work, we take a closer look at them. We characterize a wider class of constraint automata that give constrained synchronization problems in NP, which encompasses all known problems in NP. We call these automata polycyclic automata. The corresponding language class of polycyclic languages is introduced. We show various characterizations and closure properties for this new language class. We then give a criterion for NP-completeness and a criterion for polynomial time solvability for polycyclic constraint languages.

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Computational Complexity of Synchronization Under Regular Commutative Constraints

Cited by 7 publications

References 41 publications

Constrained Synchronization for Commutative Automata and Automata with Simple Idempotents

Constrained Synchronization for Commutative Automata and Automata with Simple Idempotents

Constrained Synchronization and Subset Synchronization Problems for Weakly Acyclic Automata

On a Class of Constrained Synchronization Problems in NP

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