Finite Automata and Their Decision Problems

  title={Finite Automata and Their Decision Problems},
  author={Michael O. Rabin and Dana S. Scott},
  journal={IBM J. Res. Dev.},
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.
On Finite Automata with a Time-Variant Structure
Simple Counter Machines and Number-Theoretic Problems
Theories of Automata on omega-Tapes: A Simplified Approach
Subset construction complexity for homogeneous automata, position automata and ZPC-structures
The Equivalence Problem for n-Tape Finite Automata with Simple Cycles
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.
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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.
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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
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.


The Reduction of Two-Way Automata to One-Way Automata
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 tapes
Representation of Events in Nerve Nets and Finite Automata
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
For a finite commutative ring with unit the authors determine which linear transformations M: RN—+RN can be realized by finite automata.
A variant of a recursively unsolvable problem
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 g2gigigzg2