Synchronizing Finite Automata on Eulerian Digraphs

@inproceedings{Kari2001SynchronizingFA,
  title={Synchronizing Finite Automata on Eulerian Digraphs},
  author={Jarkko Kari},
  booktitle={MFCS},
  year={2001}
}
  • J. Kari
  • Published in MFCS 24 February 2003
  • Mathematics
?erný's conjecture and the road coloring problem are two open problems concerning synchronization of finite automata. We prove these conjectures in the special case that the vertices have uniform in- and outdegrees. 

Figures from this paper

Synchronizing Automata and the Cerny Conjecture
TLDR
Some recent advances towards a solution of the Cerný conjecture are discussed and several results and open problems related to synchronizing automata are surveyed.
The Černý conjecture for one-cluster automata with prime length cycle
Slowly Synchronizing Automata and Digraphs
TLDR
Several infinite series of synchronizing automata for which the minimum length of reset words is close to the square of the number of states are presented, related to primitive digraphs with large exponent.
The Černý conjecture for automata respecting intervals of a directed graph
TLDR
This work proves the Cerný's conjecture that for every synchronizing automaton with n states there exists a reset word of length not exceeding (n - 1)2, and unifies and generalizes some earlier results obtained.
Strongly transitive automata and the Černý conjecture
The synchronization problem is investigated for a new class of deterministic automata called strongly transitive. An extension to unambiguous automata is also considered.
Synchronizing Automata of Bounded Rank
  • V. Gusev
  • Mathematics, Computer Science
    CIAA
  • 2012
We reduce the problem of synchronization of an n-state automaton with letters of rank at most r \frac{n}{2}$, such automata are strongly connected.
A Note on Synchronized Automata and Road Coloring Problem
TLDR
A relabeling method is introduced which can be used for a large class of automata to improve their "degree of synchronization" and allows, for example, to formulate the Road Coloring Conjecture in several equivalent ways.
The Synchronization Problem for Locally Strongly Transitive Automata
The synchronization problem is investigated for a new class of deterministic automata called locally strongly transitive. An application to synchronizing colorings of aperiodic graphs with a cycle of
Synchronizing quasi-Eulerian and quasi-One-Cluster Automata
We describe a new version of the so-called extension method that was used to prove quadratic upper bounds on the minimum length of reset words for various important classes of synchronizing automat...
...
...

References

SHOWING 1-10 OF 31 REFERENCES
Many-Valued Truth Functions, Cerny's Conjecture and Road Coloring
TLDR
Interconnections between many-valued truth functions and functions defined by finite deterministic automata is investigated, finding results in one theory, such as those concerning self-conjugacy of truth functions, can be applied in the other theory.
Cycles of relatively prime length and the road coloring problem
We give a partial answer to theroad coloring problem, a purely graphtheoretical question with applications in both symbolic dynamics and automata theory. The question is whether for any positive
The road-colouring problem
LetG be a finite directed graph which is irreducible and aperiodic. Assume each vertex ofG leads to at least two other vertices, and assumeG has a cycle of prime length which is a proper subset ofG.
Equivalence of topological Markov shifts
We show that any two topological Markov shifts both of whose topological entropy equals logn (for somen) are equivalent by a finitistic coding.
Synchronization of Finite Automata: Contributions to an Old Problem
  • A. Salomaa
  • Computer Science
    The Essence of Computation
  • 2002
TLDR
The results show that the study of functions of several variables may shed light also to the case where all functions considered are unary, and the questions about depth, as well as about the comparison of different notions of depth, remain open.
Utilisation de l'algèbre linéaire en théorie des automates
Techniques from linear algebra are used to study the synchronization problem in automata theory. Let A = (Q, X) be a finite automaton. Each word m in X* defines a map from Q to Q; the rank of m in A
SIMILARITY OF AUTOMORPHISMS OF THE TORUS
Abstract : The automorphisms of the Torus are rich mathematic objects. They possess interesting number theoretic, geometric, algebraic, topological, measure theoretic, probabilistic, and even
Introduction to Graph Theory
1. Fundamental Concepts. What Is a Graph? Paths, Cycles, and Trails. Vertex Degrees and Counting. Directed Graphs. 2. Trees and Distance. Basic Properties. Spanning Trees and Enumeration.
Theoretical Computer Science
TLDR
The Fully Mixed Nash Equilibrium Conjecture is valid for pure Nash equilibria and that under a certain condition, the social cost of any Nash equilibrium is within a factor of 6 + ε, of that of the fully mixed Nash equilibrium, assuming that link capacities are identical.
...
...