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.Expand
On Finite Automata with a Time-Variant Structure
  • A. Salomaa
  • Mathematics, Computer Science
  • Inf. Control.
  • 1968
Basic theory of finite automata whose state transitions and outputs depend on time is developed. A necessary and sufficient condition for a language to be accepted by such an automaton isExpand
Simple Counter Machines and Number-Theoretic Problems
It is shown that every machine in this class of deterministic two-way finite automata augmented by reversal-bounded counters operating on inputs over a one-letter alphabet can effectively be reduced to an equivalent (ordinary) finite automaton. Expand
Theories of Automata on omega-Tapes: A Simplified Approach
  • Y. Choueka
  • Computer Science, Mathematics
  • J. Comput. Syst. Sci.
  • 1974
Using a combinatorial lemma on regular sets, and a technique of attaching a control unit to a parallel battery of finite automata, a simple and transparent development of McNaughton's theory ofExpand
Subset construction complexity for homogeneous automata, position automata and ZPC-structures
A new upper bound on the number of states of the subset-automaton is established in the case of homogeneous automata and the complexity of the two basic steps of subset construction is examined depending on whether the nondeterministic automaton is an unrestricted one, an homogeneous one, a position one or a ZPC-structure. Expand
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. Expand
Finite Automata, Definable Sets, and Regular Expressions over omega^n-Tapes
  • Y. Choueka
  • Computer Science, Mathematics
  • J. Comput. Syst. Sci.
  • 1978
The theory of finite automata and regular expressions over a finite alphabet Σ is generalized to infinite tapes X = X 1 … X k, where X i, are themselves tapes of length ω n, and the equivalence of deterministic and nondeterministic automata is proved. Expand
Descriptional Complexity of Finite Automata: Concepts and Open Problems
  • J. Hromkovic
  • Mathematics, Computer Science
  • J. 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. Expand
Finite Automata with Multiplication
It is shown that the languages recognized by two-way deterministic FAM's are of tape complexity log n and time complexity n 3 . Expand
Equivalence of Infinite Behavior of Finite Automata
  • H. Alaiwan
  • Computer Science, Mathematics
  • Theor. Comput. Sci.
  • 1984
A necessary and sufficient condition of equivalence is given, which uses considerations over finite behaviors only, and an algorithm for the general case is given; its time and space complexity is better than any other existent method. Expand
  • T. Grigoryan
  • Proceedings of the YSU A: Physical and Mathematical Sciences
  • 2019
We consider sets of word tuples accepted by multitape finite automata. We use the known notation for regular expressions that describes languages accepted by one-tape automata. Nevertheless, theExpand


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 tapesExpand
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. Expand
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. Expand
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 g2gigigzg2Expand