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Winning Strategies for the Synchronization Game on Subclasses of Finite Automata

Henning Fernau, Carolina Haase, Stefan Hoffmann, Mikhail Volkov

Abstract

We exhibit a winning strategy for Synchronizer in the synchronization game on every synchronizing automaton in whose transition monoid the regular D-classes form subsemigroups

Winning Strategies for the Synchronization Game on Subclasses of Finite Automata

Abstract

We exhibit a winning strategy for Synchronizer in the synchronization game on every synchronizing automaton in whose transition monoid the regular D-classes form subsemigroups
Paper Structure (12 sections, 4 theorems, 2 equations)

This paper contains 12 sections, 4 theorems, 2 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Transition Monoids and Synchronization
  4. Structure of Semigroups in $\mathbf{DS}$
  5. Winning Strategy in Synchronization Games on DS-Automata
  6. Relations to Earlier Results and Future Work
  7. Corollaries
  8. Definite automata.
  9. Commutative automata.
  10. Weakly acyclic automata.
  11. Open Questions
  12. Acknowledgement.

Key Result

Lemma 1

A DFA is synchronizing if and only if the kernel of its transition monoid consists of constant transformations.

Theorems & Definitions (10)

  • Definition 1
  • Lemma 1
  • proof
  • Definition 2
  • Lemma 2
  • Theorem 3
  • proof
  • Definition 3
  • Lemma 4
  • proof