Complexity of suffix-free regular languages

@article{Brzozowski2017ComplexityOS,
  title={Complexity of suffix-free regular languages},
  author={Janusz A. Brzozowski and Marek Szykula},
  journal={J. Comput. Syst. Sci.},
  year={2017},
  volume={89},
  pages={270-287}
}

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References

SHOWING 1-10 OF 53 REFERENCES

Complexity of Suffix-Free Regular Languages⋆

A sequence (Lk, Lk+1 . . . ) of regular languages in some class C, where n is the state complexity of Ln, is called a stream. A stream is most complex in class C if its languages together with their

Symmetric Groups and Quotient Complexity of Boolean Operations

TLDR
The notion of uniform minimality to direct products of automata is generalized and the non-trivial connection between complexity of boolean operations and group theory is established.

Complexity of Left-Ideal, Suffix-Closed and Suffix-Free Regular Languages

TLDR
The quotient/state complexity of boolean operations, product, star, and reversal on suffix-convex languages, as well as the size of their syntactic semigroups, and the quotient complexity of their atoms are studied.

In Search of Most Complex Regular Languages

TLDR
The language stream (Un(a, b, c) | n ≥ 3) is defined by the deterministic finite automaton, where a performs a cyclic permutation of the n states, b transposes states 0 and 1, and c maps state n − 1 to state 0.

Complexity in Convex Languages

TLDR
This paper surveys the recent results on convex languages with an emphasis on complexity issues.

Most Complex Regular Right-Ideal Languages

TLDR
It is shown that there exists a sequence of regular right-ideal languages, where R n has n left quotients and is most complex among regular right ideals under the following measures of complexity.

Upper Bound on Syntactic Complexity of Suffix-Free Languages

TLDR
It is proved that the cardinality of the syntactic semigroup of a suffix-free language with \(n\) left quotients is at most \((n-1)^{n-2}+ n-2\) for \(n\geqslant 7\).

Complexity of Proper Prefix-Convex Regular Languages

TLDR
It is proved that three witness streams are required to meet all upper bounds for reversal, star, product, and boolean operations of proper suffix-convex languages, and it is conjecture on the size of the largest syntactic semigroup.

Syntactic Complexity of Bifix-Free Languages

TLDR
It is proved that the cardinality of the syntactic semigroup of a bifix-free language with state complexity n is at most \((n-1)^{n-3}+(n-2)^{ n-3}) + (n- 3)2-1 - 1, which is the minimal size of the alphabet required to meet the bound for \(n \geqslant 6\).

Quotient Complexity of Bifix-, Factor-, and Subword-free Regular Languages

TLDR
Tight upper bounds are found on the quotient complexity of intersection, union, difference, symmetric difference, concatenation, star, and reversal in these three classes of languages.
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