arXiv subjects

Felix Tschirbs

Publications and source records attributed to Felix Tschirbs.

4 recordsLinked to original sources

arXiv2026

Dynamic Planar Graph Isomorphism is in DynFO

Consider two planar graphs which are subject to edge insertions and deletions. We show that whether the two graphs are isomorphic can be maintained with first-order logic formulas and auxiliary data of polynomial size. This places the dynamic planar graph isomorphism problem into the dynamic descriptive complexity class DynFO. As a consequence, there is a dynamic constant-time parallel algorithm with polynomial-size auxiliary data which maintains whether two dynamic planar graphs are isomorphic.

cs.LO↗

arXiv2026

Algebraic Characterizations of Classes of Regular Languages in DynFO

This paper explores the fine-grained structure of classes of regular languages maintainable in fragments of first-order logic within the dynamic descriptive complexity framework of Patnaik and Immerman. A result by Hesse states that the class of regular languages is maintainable by first-order formulas even if only unary auxiliary relations can be used. Another result by Gelade, Marquardt,and Schwentick states that the class of regular languages coincides with the class of languages maintainable by quantifier-free formulas with binary auxiliary relations. We refine Hesse's result and show that with unary auxiliary data formulas with one quantifier alternation can maintain all regular languages. We then obtain precise algebraic characterizations of the classes of languages maintainable with quantifier-free formulas and positive existential formulas in the presence of unary auxiliary relations.

cs.LO↗

arXiv2024

Query maintenance under batch changes with small-depth circuits

Which dynamic queries can be maintained efficiently? For constant-size changes, it is known that constant-depth circuits or, equivalently, first-order updates suffice for maintaining many important queries, among them reachability, tree isomorphism, and the word problem for context-free languages. In other words, these queries are in the dynamic complexity class DynFO. We show that most of the existing results for constant-size changes can be recovered for batch changes of polylogarithmic size if one allows circuits of depth O(log log n) or, equivalently, first-order updates that are iterated O(log log n) times.

cs.LO↗

arXiv2022

Iltis: Learning Logic in the Web

The Iltis project provides an interactive, web-based system for teaching the foundations of formal methods. It is designed with the objective to allow for simple inclusion of new educational tasks; to pipeline such tasks into more complex exercises; and to allow simple inclusion and cascading of feedback mechanisms. Currently, exercises for many typical automated reasoning workflows for propositional logic, modal logic, and some parts of first-order logic are covered. Recently, Iltis has reached a level of maturity where large parts of introductory logic courses can be supplemented with interactive exercises. Sample interactive course material has been designed and used in courses over the last years, many of them with more than 300 students. We invite all readers to try out Iltis: https://iltis.cs.tu-dortmund.de

cs.LO↗