Commutative Regular Languages – Properties and State Complexity

Hoffmann, Stefan

doi:10.1007/978-3-030-21363-3_13

Cited by 14 publications

(26 citation statements)

References 11 publications

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“…Upper Bound Lower Bound References πΓ pU q, Γ Ď Σ n n [14,17] U ¡ V mintp2nmq 1. Overview of results for commutative regular languages.…”

Section: Operationmentioning

confidence: 99%

“…In [8] the minimal commutative automaton was introduced, which can be associated with every commutative regular language. This automaton played a crucial role in [14,15] to derive the bounds mentioned in Table 1. Here, we will investigate the subclass of those language for which the minimal commutative automaton is in fact the smallest automaton recognizing a given commutative language.…”

Section: Operationmentioning

confidence: 99%

“…The minimal commutative automaton was introduced in [8] to investigate the learnability of commutative languages. In [14,15] this construction was used to define the index and period vector and in the derivation of the state complexity bounds mentioned in Table 1.…”

Section: Preliminariesmentioning

confidence: 99%

“…The next definition from [14,15] generalizes the notion of a cyclic and noncyclic part for unary automata [24], and the notion of periodic language [6,14,15]. Definition 3 (index and period vector).…”

Section: Preliminariesmentioning

confidence: 99%

“…In [14,15,16,17] the state complexity of these operations was investigated for commutative regular languages. The results are summarized in Table 1.…”

Section: Introductionmentioning

confidence: 99%

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Commutative Regular Languages with Product-Form Minimal Automata

Hoffmann¹

2021

Preprint

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We introduce a subclass of the commutative regular languages that is characterized by the property that the state set of the minimal deterministic automaton can be written as a certain Cartesian product. This class behaves much better with respect to the state complexity of the shuffle, for which we find the bound 2nm if the input languages have state complexities n and m, and the upward and downward closure and interior operations, for which we find the bound n. In general, only the bounds p2nmq |Σ| and n |Σ| are known for these operations in the commutative case. We prove different characterizations of this class and present results to construct languages from this class. Lastly, in a slightly more general setting of partial commutativity, we introduce other, related, language classes and investigate the relations between them.

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“…Upper Bound Lower Bound References πΓ pU q, Γ Ď Σ n n [14,17] U ¡ V mintp2nmq 1. Overview of results for commutative regular languages.…”

Section: Operationmentioning

confidence: 99%

Section: Operationmentioning

confidence: 99%

Section: Preliminariesmentioning

confidence: 99%

Section: Preliminariesmentioning

confidence: 99%

“…In [14,15,16,17] the state complexity of these operations was investigated for commutative regular languages. The results are summarized in Table 1.…”

Section: Introductionmentioning

confidence: 99%

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Commutative Regular Languages with Product-Form Minimal Automata

Hoffmann¹

2021

Preprint

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Computational Complexity of Synchronization Under Regular Commutative Constraints

Hoffmann

2020

Lecture Notes in Computer Science

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The constrained synchronization problem (CSP) asks for a synchronizing word of a given input automaton contained in a regular set of constraints. It could be viewed as a special case of synchronization of a discrete event system under supervisory control. Here, we study the computational complexity of this problem for the class of sparse regular constraint languages. We give a new characterization of sparse regular sets, which equal the bounded regular sets, and derive a full classification of the computational complexity of CSP for letter-bounded regular constraint languages, which properly contain the strictly bounded regular languages. Then, we introduce strongly self-synchronizing codes and investigate CSP for bounded languages induced by these codes. With our previous result, we deduce a full classification for these languages as well. In both cases, depending on the constraint language, our problem becomes NP-complete or polynomial time solvable.

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State Complexity Bounds for the Commutative Closure of Group Languages

Hoffmann

2020

Lecture Notes in Computer Science

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Commutative Regular Languages – Properties and State Complexity

Cited by 14 publications

References 11 publications

Commutative Regular Languages with Product-Form Minimal Automata

Commutative Regular Languages with Product-Form Minimal Automata

Computational Complexity of Synchronization Under Regular Commutative Constraints

State Complexity Bounds for the Commutative Closure of Group Languages

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