# Finite Automata and Their Decision Problems

@article{Rabin1959FiniteAA, title={Finite Automata and Their Decision Problems}, author={Michael O. Rabin and Dana S. Scott}, journal={IBM J. Res. Dev.}, year={1959}, volume={3}, pages={114-125} }

Finite automata are considered in this paper as instruments for classifying finite tapes. [... ] Key Method Various generalizations of the notion of an automaton are introduced and their relation to the classical automata is determined. Some decision problems concerning automata are shown to be solvable by effective algorithms; others turn out to be unsolvable by algorithms. Expand

## 1,812 Citations

Simple Counter Machines and Number-Theoretic Problems

- Computer Science, MathematicsJ. Comput. Syst. Sci.
- 1979

Theories of Automata on omega-Tapes: A Simplified Approach

- MathematicsJ. Comput. Syst. Sci.
- 1974

Subset construction complexity for homogeneous automata, position automata and ZPC-structures

- Computer ScienceTheor. Comput. Sci.
- 2001

The Equivalence Problem for n-Tape Finite Automata with Simple Cycles

- Computer Science, MathematicsFSTTCS
- 1987

The equivalence problem for 2-tape deterministic finite automata was shown decidable by Bird in 1973, and it is shown that it is decidable for the restricted class of simple automata.

Finite Automata, Definable Sets, and Regular Expressions over omega^n-Tapes

- Computer Science, MathematicsJ. Comput. Syst. Sci.
- 1978

Descriptional Complexity of Finite Automata: Concepts and Open Problems

- Computer ScienceJ. Autom. Lang. Comb.
- 2002

It is argued that if one wishes a renaissance of automata theory, then one should prefer to return to the investigation of the fundamental, classical problems of Automata theory rather then searching for new applications and defining numerous questionable modifications of basic models.

Equivalence of Infinite Behavior of Finite Automata

- Mathematics, Computer ScienceTheor. Comput. Sci.
- 1984

SOME RESULTS ON REGULAR EXPRESSIONS FOR MULTITAPE FINITE AUTOMATA

- Computer Science, MathematicsProceedings of the YSU A: Physical and Mathematical Sciences
- 2019

It is shown that the introduced algebra is a Kleene algebra and some known results for the algebra of events accepted by one-tape finite automata are valid in this case too.

Deterministic Input-Reversal and Input-Revolving Finite Automata

- Computer ScienceLATA
- 2008

It is shown that the family of languages accepted by deterministic right-revolving finite automata is an anti-AFL which is not closed under reversal and intersection.

## References

SHOWING 1-5 OF 5 REFERENCES

The Reduction of Two-Way Automata to One-Way Automata

- Computer ScienceIBM J. Res. Dev.
- 1959

Rabin has proved 1,2 that two-way finite automata, which are allowed to move in both directions along their input tape, are equivalent to one-way automata as far as the classification of input tapesâ€¦

Representation of Events in Nerve Nets and Finite Automata

- Computer Science
- 1951

This memorandum is devoted to an elementary exposition of the problems and of results obtained on the McCulloch-Pitts nerve net during investigations in August 1951.

Linear automaton transformations

- Mathematics
- 1958

For a finite commutative ring with unit the authors determine which linear transformations M: RNâ€”+RN can be realized by finite automata.

A variant of a recursively unsolvable problem

- Mathematics
- 1946

By a string on a, 6 we mean a row of a's and 6's such as baabbbab. I t may involve only a, or 6, or be null. If, for example, gi, g2, gz represent strings baby aa, b respectively, string g2gigigzg2â€¦