Nondeterministic State Complexity for Suffix-Free Regular Languages

@inproceedings{Han2010NondeterministicSC,
  title={Nondeterministic State Complexity for Suffix-Free Regular Languages},
  author={Yo-Sub Han and Kai Salomaa},
  booktitle={DCFS},
  year={2010}
}
We investigate the nondeterministic state complexity of basic operations for suffix-free regular languages. The nondeterministic state complexity of an operation is the number of states that are necessary and sufficient in the worst-case for a minimal nondeterministic finite-state automaton that accepts the language obtained from the operation. We consider basic operations (catenation, union, intersection, Kleene star, reversal and complementation) and establish matching upper and lower bounds… 

Tables from this paper

Nondeterministic Complexity of Operations on Free and Convex Languages

The most interesting result is the describing of a proper suffix-convex language over a five-letter alphabet meeting the upper bound \(2^n\) for complementation.

Nondeterministic Complexity of Operations on Closed and Ideal Languages

For the operations of union, intersection, complementation, concatenation, square, star, and reversal, the tight upper bounds for all considered classes are got.

State Complexity of Combined Operations for Suffix-free Regular Languages

This thesis focuses on estimating the state complexities of combined operations of prefix free regular languages for individual and combined operations for suffixfree regular languages.

Complement on Prefix-Free, Suffix-Free, and Non-Returning NFA Languages

It is proved that the tight bound on the nondeterministic state complexity of complementation on prefix-free and suffix-free languages is 2 n − 1, and it is tight already in the binary case.

A Survey on Fooling Sets as Effective Tools for Lower Bounds on Nondeterministic Complexity

It is shown that, in spite of the fact that the difference between the size of the largest fooling set and the nondeterministic state complexity may be arbitrarily large, the Fooling set lower bound methods work in many cases.

A Review on State Complexity of Individual Operations

This report reviews some of the results of state complexity of individual operations for regular and some subregular languages on the basis of subset construction and nondeterministic state complexity.

A Survey on Operational State Complexity

In this survey, the state complexities of individual regularity preserving language operations on regular and some subregular languages are reviewed and the combination of individual operations are revisited.

References

SHOWING 1-10 OF 27 REFERENCES

Nondeterministic State Complexity of Basic Operations for Prefix-Free Regular Languages

This work establishes the precise state complexity of catenation, union, intersection, Kleene star, reversal and complementation for prefix-free regular languages.

State complexity of basic operations on suffix-free regular languages

Unary Language Operations and Their Nondeterministic State Complexity

The costs, in terms of states, of operations on infinite and finite unary regular languages where the languages are represented by nondeterministic finite automata are investigated, in particular, Boolean operations, concatenation, iteration, and λ-free iteration.

Nondeterministic Descriptional Complexity Of Regular Languages

Bounds are shown for Boolean operations, catenation operations – concatenation, iteration, λ-free iteration – and the reversal on finite and infinite regular languages over unary and arbitrary alphabets.

State complexity of concatenation and complementation

The upper bounds on the state complexity of concatenation are also tight in the case that the first automaton has more than one accepting state, and the entire range of complexities, up to the known upper bound can be produced.

The State Complexities of Some Basic Operations on Regular Languages

State complexity of some operations on binary regular languages

State Complexity of Union and Intersection of Finite Languages

The upper bounds based on the structural properties of minimal deterministic finite-state automata for finite languages show that the upper bounds are tight if the authors have a variable sized alphabet that can depend on the size of input DFAs.

Unary Language Operations, State Complexity and Jacobsthal's Function

This paper gives the cost, in terms of states, of some basic operations on regular languages in the unary case (where the alphabet contains only one symbol) by explicitly determining the number of states in the noncyclic and cyclic parts of the resulting automata.

On the state complexity of reversals of regular languages