P(l)aying for Synchronization

TL;DR

This paper explores synchronization games on automata where players compete to synchronize or hinder synchronization, and analyzes the complexity of cost-constrained synchronization problems.

Contribution

It introduces the concept of synchronization games, studies their properties, and determines the complexity of synchronization costs within automata.

Findings

Synchronization games are formally defined and analyzed.

The complexity of cost-bounded synchronization problems is established.

Open questions for future research are proposed.

Abstract

Two topics are presented: synchronization games and synchronization costs. In a synchronization game on a deterministic finite automaton, there are two players, Alice and Bob, whose moves alternate. Alice wants to synchronize the given automaton, while Bob aims to make her task as hard as possible. We answer a few natural questions related to such games. Speaking about synchronization costs, we consider deterministic automata in which each transition has a certain price. The problem is whether or not a given automaton can be synchronized within a given budget. We determine the complexity of this problem. We also formulate a few open questions.