# 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…

## 29 Citations

### Descriptional Complexity of (Un)ambiguous Finite State Machines and Pushdown Automata

- Computer ScienceRP
- 2010

This paper summarizes and discusses developments relevant to (un)ambiguous finite automata and pushdown automata problems from the descriptional complexity point of view and draws attention to the big picture and some of the main ideas involved.

### Incomplete operational transition complexity of regular languages

- Computer ScienceInf. Comput.
- 2015

### Limitations of lower bound methods for deterministic nested word automata

- Computer ScienceInf. Comput.
- 2011

### On Inverse Operations and Their Descriptional Complexity

- MathematicsDCFS
- 2012

It turns out, that in most cases the authors obtain exponential upper and lower bounds that are asymptotically close, for the investigated inverse language operation problems.

### Simplifying Nondeterministic Finite Cover Automata

- Computer ScienceAFL
- 2014

It is shown that minimization can be as hard as minimizing NFAs for regular languages, even in the case of NFCAs using unary alphabets, and how to adapt the methods used to reduce, or minimize the size of NFAs/DFCA/l-DFCAs, for simplifying NFCAs/ l-NFCAs.

### Operational State Complexity of Deterministic Unranked Tree Automata

- Computer ScienceDCFS
- 2010

It is shown that (n+1) ( (m-1)2^n-2^(n- 1) )-1 vertical states are sufficient, and necessary in the worst case, to recognize the concatenation of tree languages recognized by (strongly or weakly) deterministic automata with, respectively, m and n vertical states.

### On the descriptional and algorithmic complexity of regular languages

- Computer Science
- 2010

The present work deals with mathematical models of computational processes, namely on finite automata, and model the observable behavior of a vending machine as a set of sequences over some finite alphabet.

### Transformations Between Different Types of Unranked Bottom-Up Tree Automata

- Computer ScienceDCFS
- 2010

Upper and lower bounds for the state complexity of conversions between different types of unranked tree automata are established and the alternative syntactic definition of determinism is considered.

### Transformations Between Different Models of Unranked Bottom-Up Tree Automata

- Computer ScienceFundam. Informaticae
- 2011

It is established upper and lower bounds for the state complexity of conversions between different types of unranked tree automata and the alternative syntactic definition of determinism introduced by Cristau et al.

## References

SHOWING 1-10 OF 73 REFERENCES

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

- Computer Science
- 2009

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

- Computer ScienceInt. J. Comput. Math.
- 1990

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

- Computer ScienceCIAA'02
- 2002

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.

### Optimal Simulations Between Unary Automata

- Computer ScienceSTACS
- 1998

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

- Computer ScienceSIAM J. Comput.
- 1993

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

- Mathematicscomputational complexity
- 2005

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

- Computer Science, MathematicsMFCS
- 1992

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

- Computer ScienceInt. J. Found. Comput. Sci.
- 1991

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

- Computer ScienceLATA
- 2007

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.