State Complexity of Concatenation and Complementation

Jirásek, Jozef; Jirásková, Galina; Szabari, Alexander

doi:10.1142/s0129054105003133

Cited by 59 publications

(24 citation statements)

References 18 publications

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“…In [15] it has been shown that all values from log n to 2 n can be reached, however, appropriate automata have been defined over a growing alphabet of size 2 n+1 . In this section, we prove that this result still holds for a fixed five-letter alphabet.…”

Section: Complementmentioning

confidence: 99%

“…Motivated by the magic number problem for nfa-to-dfa construction, we examined a similar question for complements of regular languages in [15]. Using a growing alphabet of size 2 n+1 we proved that all values in the range from log n to 2 n can be obtained as the nondeterministic state complexity of the complement of an n-state nfa language.…”

Section: Introductionmentioning

confidence: 99%

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The Ranges of State Complexities for Complement, Star, and Reversal of Regular Languages

Jirásková

2014

Int. J. Found. Comput. Sci.

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We examine the deterministic and nondeterministic state complexity of complements, stars, and reversals of regular languages. Our results are as follows:(1) The nondeterministic state complexity of the complement of an n-state nfa language over a five-letter alphabet may reach each value from log n to 2 n .(2) The state complexity of the star (reversal) of an n-state dfa language over a growing alphabet may reach each value from 1 to 3 4 · 2 n (from log n to 2 n , respectively). (3) The nondeterministic state complexity of the star (reversal) of an n-state nfa binary language may reach each value from 1 to n + 1 (from n − 1 to n + 1, respectively).We also obtain some partial results on the nondeterministic state complexity of complements of binary regular languages. As a bonus, we get an exponential number of values that are non-magic in the binary case.

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Section: Complementmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The Ranges of State Complexities for Complement, Star, and Reversal of Regular Languages

Jirásková

2014

Int. J. Found. Comput. Sci.

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“…Many results related to the state complexity of various operations on formal languages have been examined. We note in particular that the state complexity of concatenation was obtained by Maslov [10] and further studied by Yu et al [16] and Jirásek et al [7], who determined the effect of the number of final states on the state complexity. The state complexity of concatenation over a unary alphabet was considered by Yu et al [16] and subsequently by Pighizzini and Shallit [11], while Holzer and Kutrib [6] have studied the state complexity of concatenation with respect to nondeterministic finite automata (NFA).…”

Section: Introductionmentioning

confidence: 83%

State complexity of power

Domaratzki

Okhotin

2009

Theoretical Computer Science

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a b s t r a c tThe number of states in a deterministic finite automaton (DFA) recognizing the language L k , where L is regular language recognized by an n-state DFA, and k 2 is a constant, is shown to be at most n2 (k−1)n and at least (n − k)2 (k−1)(n−k) in the worst case, for every n > k and for every alphabet of at least six letters. Thus, the state complexity of L k is Θ(n2 (k−1)n ). In the case k = 3 the corresponding state complexity function for L 3 is determined as 6n−3 8 4 n − (n − 1)2 n − n with the lower bound witnessed by automata over a four-letter alphabet. The nondeterministic state complexity of L k is demonstrated to be nk. This bound is shown to be tight over a two-letter alphabet.

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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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State Complexity of Concatenation and Complementation

Cited by 59 publications

References 18 publications

The Ranges of State Complexities for Complement, Star, and Reversal of Regular Languages

The Ranges of State Complexities for Complement, Star, and Reversal of Regular Languages

State complexity of power

State complexity of deletion and bipolar deletion

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