Year: 2017
Type: preprint
Abstract: We study extremal and algorithmic questions of subset and careful synchronization in monotonic automata. We show that several synchronization problems that are hard in general automata can be solved in polynomial time in monotonic automata, even without knowing a linear order of the states preserved by the transitions. We provide asymptotically tight bounds on the maximum length of a shortest word synchronizing a subset of states in a monotonic automaton and a shortest word carefully synchronizing a partial monotonic automaton. We provide a complexity framework for dealing with problems for monotonic weakly acyclic automata over a three-letter alphabet, and use it to prove NP-completeness and inapproximability of problems such as {\sc Finite Automata Intersection} and the problem of computing the rank of a subset of states in this class. We also show that checking whether a monotonic partial automaton over a four-letter alphabet is carefully synchronizing is NP-hard. Finally, we give a simple necessary and sufficient condition when a strongly connected digraph with a selected subset of vertices can be transformed into a deterministic automaton where the corresponding subset of states is synchronizing.
Source: arXiv (Cornell University)
Authors: Ryzhikov, Andrew, Shemyakov, Anton
Institutions: National Academy of Sciences of Belarus, Paris-Est Sup, Laboratoire des Sciences pour la Conception, l'Optimisation et la Production, United Institute of Informatics Problems, Laboratoire d'Informatique Gaspard-Monge, Pôle de recherche et d'enseignement supérieur Université Paris-Est, Université Grenoble Alpes, Belarusian State University
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2952266151