On the Bounds for State-Set Size in the Proofs of Equivalence Between Deterministic, Nondeterministic, and Two-Way Finite Automata

@article{Moore1971OnTB,
  title={On the Bounds for State-Set Size in the Proofs of Equivalence Between Deterministic, Nondeterministic, and Two-Way Finite Automata},
  author={F. Richard Moore},
  journal={IEEE Transactions on Computers},
  year={1971},
  volume={C-20},
  pages={1211-1214}
}
  • F. R. Moore
  • Published 1 October 1971
  • Mathematics, Computer Science
  • IEEE Transactions on Computers
The bounds on state-set size in the proofs of the equivalence between nondeterministic and deterministic finite automata and between two-way and one-way deterministic finite automata are considered. It is shown that the number of states in the subset machine in the first construction cannot be reduced for certain cases. It is also shown that the number of states in the one-way automation constructed in the second proof may be reduced only slightly. 
Equivalence Problem of Non-Deterministic Finite Automata
  • A. Nozaki
  • Computer Science, Mathematics
    J. Comput. Syst. Sci.
  • 1979
TLDR
It is shown that the optimal bound to the lengths of input strings to be examined for checking equivalence of non-deterministic automata is of order O (2 m + 2 n ), where m and n are the state numbers of the automata under question.
A Technique for Proving Lower Bounds on the Size of Sweeping Automata
  • H. Leung
  • Mathematics, Computer Science
    J. Autom. Lang. Comb.
  • 2009
TLDR
This paper proposes a technique based on the work in [6] for establishing lower bounds on the size of sweeping automata, and shows that Sipser's technique is a special case of this method.
Lower Bounds on the Size of Sweeping Automata
TLDR
It is shown that any sweeping automaton for the language (L$)* has to have at least √m/2 states whenever the nondeterministic message complexity of L is at least m, the first general method to establish lower bounds on the conciseness of sweeping automata.
On the descriptional complexity of finite automata with modified acceptance conditions
We consider deterministic and nondeterministic finite automata with acceptance conditions that rely on the whole history of a computation on a given word and not only on the last state of the
On the Size of Two-Way Reasonable Automata for the Liveness Problem
TLDR
This paper extends the study of the descriptional complexity of ras solving the liveness problem, showing several lower and upper bounds for different choices of allowed atomic predicates and connectors.
Complementing two-way finite automata
We study the relationship between the sizes of two-way finite automata accepting a language and its complement. In the deterministic case, for a given automaton (2dfa) with n states, we build an
Tight Lower Bounds on the Size of Sweeping Automata
  • H. Leung
  • Computer Science, Mathematics
    J. Comput. Syst. Sci.
  • 2001
TLDR
It is shown that for each positive integer n, there is a nondeterministic finite automaton An over a two-letter alphabet such that An has n states, whereas the smallest equivalent nondegenerate sweeping automaton has 2n states.
From Finite Automata to Regular Expressions and Back - A Summary on Descriptional Complexity
TLDR
Results on upper and lower bounds on the conversion of finite automata to regular expressions and vice versa are summarized and results on recent results on the average case descriptional complexity bounds are reported.
Nondeterministic State Complexity of Star-Free Languages
We investigate the nondeterministic state complexity of several operations on finite automata accepting star-free languages. It turns out that in most cases exactly the same tight bounds as for
From Finite Automata to Regular Expressions and Back-A Summary on Descriptional Complexity
TLDR
Results on upper and lower bounds on the conversion of finite automata to regular expressions and vice versa are summarized and recent results on the average case descriptional complexity bounds are reported on.
...
1
2
3
4
5
...

References

SHOWING 1-3 OF 3 REFERENCES
Finite Automata and Their Decision Problems
TLDR
Finite automata are considered as instruments for classifying finite tapes as well as generalizations of the notion of an automaton are introduced and their relation to the classical automata is determined.
Mathematical theory of automata
Gedanken-Experiments on Sequential Machines