Szymon Toruńczyk ; Thomas Zeume - Register Automata with Extrema Constraints, and an Application to Two-Variable Logic

lmcs:7077 - Logical Methods in Computer Science, March 23, 2022, Volume 18, Issue 1 - https://doi.org/10.46298/lmcs-18(1:42)2022
Register Automata with Extrema Constraints, and an Application to Two-Variable Logic

Authors: Szymon Toruńczyk ; Thomas Zeume

We introduce a model of register automata over infinite trees with extrema constraints. Such an automaton can store elements of a linearly ordered domain in its registers, and can compare those values to the suprema and infima of register values in subtrees. We show that the emptiness problem for these automata is decidable. As an application, we prove decidability of the countable satisfiability problem for two-variable logic in the presence of a tree order, a linear order, and arbitrary atoms that are MSO definable from the tree order. As a consequence, the satisfiability problem for two-variable logic with arbitrary predicates, two of them interpreted by linear orders, is decidable.


Volume: Volume 18, Issue 1
Published on: March 23, 2022
Accepted on: October 8, 2021
Submitted on: January 12, 2021
Keywords: Computer Science - Logic in Computer Science,Computer Science - Formal Languages and Automata Theory


Share

Consultation statistics

This page has been seen 275 times.
This article's PDF has been downloaded 246 times.