Operational State Complexity under Parikh Equivalence

Lavado, Giovanna J.; Pighizzini, Giovanni; Seki, Shinnosuke

doi:10.1007/978-3-319-09704-6_26

Cited by 11 publications

(4 citation statements)

References 17 publications

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“…A summary of our results can be found in Table 1. The precise bound of the former result improves a recent result shown in [9], and the latter result on the complementation answers an open question stated in [9], too.…”

Section: Introductionsupporting

confidence: 83%

On the Descriptional Complexity of Operations on Semilinear Sets

Beier

Holzer

Kutrib

2017

Electron. Proc. Theor. Comput. Sci.

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We investigate the descriptional complexity of operations on semilinear sets. Roughly speaking, a semilinear set is the finite union of linear sets, which are built by constant and period vectors. The interesting parameters of a semilinear set are: (i) the maximal value that appears in the vectors of periods and constants and (ii) the number of such sets of periods and constants necessary to describe the semilinear set under consideration. More precisely, we prove upper bounds on the union, intersection, complementation, and inverse homomorphism.

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Section: Introductionsupporting

confidence: 83%

On the Descriptional Complexity of Operations on Semilinear Sets

Beier

Holzer

Kutrib

2017

Electron. Proc. Theor. Comput. Sci.

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“…the Parikh image of the languages one can prove a better conversion bound. Namely, in [8] it was shown that for each NFA with n states a Parikh equivalent DFA with e O( √ n log n) states can be constructed and that this bound is asymptotically tight. Thus, in our setting this result reads as follows: Theorem 3.…”

Section: Variants Of Nondeterministic Jumping Finite Automatamentioning

confidence: 99%

Nondeterministic Right One-Way Jumping Finite Automata (Extended Abstract)

Beier

Holzer

2019

Descriptional Complexity of Formal Systems

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Right one-way jumping finite automata are deterministic devices that process their input in a discontinuous fashion. We generalise these devices to nondeterministic machines. More precisely we study the impact on the computational power of these machines when allowing multiple initial states and/or a nondeterministic transition function including spontaneous or λ-transitions. We show inclusion relations and incomparability results of the induced language families. Since for rightone way jumping devices the use of spontaneous transitions is subject to different natural interpretations, we also study this subject in detail, showing that most interpretations are equivalent to each other and lead to the same language families. Finally we also study inclusion and incomparability results to classical language families and to the families of languages accepted by finite automata with translucent letters.

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“…The precise worst case state complexity of many basic language operations has been established; see e.g. [2,5,8,14,17,23,25,27,31,33,37]. Also there has been much work on the state complexity of combinations of basic language operations [3,7,9,10,18,32].…”

Section: Introductionmentioning

confidence: 99%

State complexity of deletion and bipolar deletion

Han

Salomaa

2015

Acta Informatica

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It is well known that the language obtained by deleting an arbitrary language from a regular language is regular. We give an upper bound for the state complexity of deleting an arbitrary language from a regular language and a matching lower bound. We show that the state complexity of deletion is n · 2 n−1 [respectively, (n + 1 2 ) · 2 n − 2] when using complete (respectively, incomplete) deterministic finite automata. We show that the state complexity of bipolar deletion has an upper bound n n [respectively (n + 1) n − 1] when using complete (respectively, incomplete) deterministic finite automata. In both cases we give almost matching lower bounds.

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Operational State Complexity under Parikh Equivalence

Cited by 11 publications

References 17 publications

On the Descriptional Complexity of Operations on Semilinear Sets

On the Descriptional Complexity of Operations on Semilinear Sets

Nondeterministic Right One-Way Jumping Finite Automata (Extended Abstract)

State complexity of deletion and bipolar deletion

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