Descriptional and Computational Complexity of Finite Automata

@inproceedings{Holzer2009DescriptionalAC,
  title={Descriptional and Computational Complexity of Finite Automata},
  author={Markus Holzer and Martin Kutrib},
  booktitle={LATA},
  year={2009}
}
Over the last half century, a vast literature documenting the importance of deterministic, nondeterministic, and alternating finite automata as an enormously valuable concept has been developed. In the present paper, we tour a fragment of this literature. Mostly, we discuss developments relevant to finite automata related problems like, for example, (i) simulation of and by several types of finite automata, (ii) standard automata problems such as, e.g., fixed and general membership, emptiness… 

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References

SHOWING 1-10 OF 73 REFERENCES

NONDETERMINISTIC FINITE AUTOMATA — RECENT RESULTS ON THE DESCRIPTIONAL AND COMPUTATIONAL COMPLEXITY

TLDR
This paper discusses recent developments relevant to NFAs related problems like, for example, simulation of and by several types of finite automata, minimization and approximation, size estimation of minimal NFAs, and state complexity of language operations.

Constructions for alternating finite automata

TLDR
Direct constructions for the usual language theoretic operations in terms of alternating finite automata are presented and minimization and direct transformations between alternating, non-deterministic, and deterministic finite Automata are discussed.

State complexity of basic operations on nondeterministic finite automata

TLDR
It turns out that the state complexities of operations on NFAs and deterministic finite automata (DFA) are quite different, for example, the reversal and concatenation have exponential state complexity on DFAs but linear complexity onNFAs.

Minimizing finite automata is computationally hard

Optimal Simulations Between Unary Automata

TLDR
This work considers the problem of computing the costs — in terms of states — of optimal simulations between different kinds of finite automata recognizing unary languages and shows that, given a unary n-state two-way nondeterministic automaton, one can construct an equivalent O(n 2)-state one-way deterministic automata.

Minimal NFA Problems are Hard

TLDR
This work studies the complexity of decision problems for finite automata and presents many fundamental decision problems which are computationally intractable even when the input is a DFA or a NFA with limited nondeterminism.

NC1: The automata-theoretic viewpoint

TLDR
It is shown that any two separable such language classes can be separated by a regular language, and the statement of a conjecture whose proof would refine and then resolve most open questions about this internal structure of non-uniformNC1 is concluded.

The Emptiness Problem for Intersections of Regular Languages

TLDR
The case, when m is bounded by a function in the input length, i.e., in the size and number of the automata, is considered, which gets complete problems for nondeterministic space-bounded and timespace- bounded complexity classes.

The Structure and Complexity of Minimal NFA's over a Unary Alphabet

TLDR
The main result is that DFA → NFA, when the input is a unary cyclic DFA (a DFA whose graph is a simple cycle), is in NP but not in P unless NP ⊑ DTIME(nO(log n)).

Computational Complexity of NFA Minimization for Finite and Unary Languages

TLDR
It is shown that the corresponding problem for unary regular languages in general, i.e., not limited to the cyclic case, can be approximated in polynomial time within a performance ratio of O( √ n), where n is the number of states of the given deterministic finite state machine.
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