On the Square of Regular Languages

Čevorová, Kristína; Jirásková, Galina; Krajňáková, Ivana

doi:10.1007/978-3-319-08846-4_10

Cited by 9 publications

(9 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, to prove distinguishability a third letter was needed, so the binary case was left open. Surprisingly, in [2], we were unable to prove the tightness of the upper bound in the case of n − 1 final states.…”

Section: Introductionmentioning

confidence: 79%

See 1 more Smart Citation

Square on Deterministic, Alternating, and Boolean Finite Automata

Krajňáková

Jirásková

2017

Descriptional Complexity of Formal Systems

Self Cite

View full text Add to dashboard Cite

We investigate the state complexity of the square operation on languages represented by deterministic, alternating, and Boolean automata. For each k such that 1 ≤ k ≤ n−2, we describe a binary language accepted by an n-state DFA with k final states meeting the upper bound n2 n − k2 n−1 on the state complexity of its square. We show that in the case of k = n − 1, the corresponding upper bound cannot be met. Using the DFA witness for square with 2 n states where half of them are final, we get the tight upper bounds on the complexity of the square operation on alternating and Boolean automata.

show abstract

Section: Introductionmentioning

confidence: 79%

“…The problem seems to be interesting per se. Previously in [2], we tried to use Rampersad's binary witness for square [8] with k final states instead of original one. We were able to show the reachability of n2 n − k2 n−1 states in the subset automaton of an NFA for its square.…”

Section: Introductionmentioning

confidence: 99%

Square on Deterministic, Alternating, and Boolean Finite Automata

Krajňáková

Jirásková

2017

Descriptional Complexity of Formal Systems

Self Cite

View full text Add to dashboard Cite

show abstract

“…Surprisingly, in Ref. [2], we were unable to prove the tightness of the upper bound in the case of n − 1 final states.…”

Section: Introductionmentioning

confidence: 79%

“…Previously in Ref. [2], we tried to use Rampersad's binary witness for square [11] with k final states instead of the original one. We were able to show the reachability of n2 n − k2 n−1 states in the subset automaton of an NFA for its square.…”

Section: Introductionmentioning

confidence: 99%

Square on Deterministic, Alternating, and Boolean Finite Automata

Jirásková

Krajňáková

2019

Int. J. Found. Comput. Sci.

Self Cite

View full text Add to dashboard Cite

We investigate the state complexity of the square operation on languages represented by deterministic, alternating, and Boolean automata. For each [Formula: see text] such that [Formula: see text], we describe a binary language accepted by an [Formula: see text]-state deterministic finite automaton with [Formula: see text] final states meeting the upper bound [Formula: see text] on the state complexity of its square. We show that in the case of [Formula: see text], the corresponding upper bound cannot be met. Using the binary deterministic witness for square with [Formula: see text] states where half of them are final, we get the tight upper bounds [Formula: see text] and [Formula: see text] on the complexity of the square operation on alternating and Boolean automata, respectively.

show abstract

“…She studied the star operation on unary regular languages, and proved that there are two linear segments of magic numbers in the range from 1 to (n − 1) 2 + 1, that is, of values that cannot be met by the state complexity of the star of a unary language accepted by a minimal n-state DFA. On the other hand, she proved that for the square operation in the unary case no magic numbers exist [19]. Another example of the existence of magic numbers for symmetric difference NFAs was presented by Zijl [17], but they could possibly be trivial.…”

Section: Introductionmentioning

confidence: 99%