arXiv subjects

Thomas Zeume

Publications and source records attributed to Thomas Zeume.

At least 19 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

Cross-Course Generalizability of SRL-Aligned Predictive Models Using Digital Learning Traces

STEM dropout rates remain high at universities, particularly in computer science programs with theory-intensive courses. Digital learning environments now capture rich behavioral data that could help identify struggling students early, yet the generalizability of data-driven prediction models across courses and institutions remains uncertain. Guided by self-regulated learning (SRL) theory, this study analyzed multimodal digital-trace data from three undergraduate theoretical computer science courses (N1 = 137, N2 = 104, N3 = 148) at two universities. Weekly SRL-aligned digital-trace indicators were modeled using Elastic Net, Random Forest, and XGBoost to evaluate predictive performance over time and across settings, and model calibration both within and across courses. Early prediction of at-risk students was feasible, with SRL-related behaviors such as time management, effort regulation, and sustained engagement emerging as key predictors. While Random Forest achieved the highest in-sample accuracy, Elastic Net generalized more robustly across contexts. Out-of-sample accuracy and calibration declined between institutions with different base rates, underscoring the contextual nature of predictive analytics in higher education. These findings suggest that digital learning traces enable early identification of at-risk students within courses, but generalizing predictive models beyond their original context requires caution, particularly if the at-risk rates differ between contexts.

cs.CY↗

arXiv2026

Identifying and Explaining (Non-)Equivalence of First-Order Logic Formulas

First-order logic is the basis for many knowledge representation formalisms and methods. Providing technological support for learning to write first-order formulas for natural language specifications requires methods to test formulas for (non-)equivalence and to provide explanations for non-equivalence. We propose such methods based on both theoretical insights and existing tools, implement them, and report on experiments testing their effectiveness on a large educational data set with > 100.000 pairs of first-order formulas.

cs.LO↗

arXiv2026

NILE: Formalizing Natural-Language Descriptions of Formal Languages

This paper explores how natural-language descriptions of formal languages can be compared to their formal representations and how semantic differences can be explained. This is motivated from educational scenarios where learners describe a formal language (presented, e.g., by a finite state automaton, regular expression, pushdown automaton, context-free grammar or in set notation) in natural language, and an educational support system has to (1) judge whether the natural-language description accurately describes the formal language, and to (2) provide explanations why descriptions are not accurate. To address this question, we introduce a representation language for formal languages, Nile, which is designed so that Nile expressions can mirror the syntactic structure of natural-language descriptions of formal languages. Nile is sufficiently expressive to cover a broad variety of formal languages, including all regular languages and fragments of context-free languages typically used in educational contexts. Generating Nile expressions that are syntactically close to natural-language descriptions then allows to provide explanations for inaccuracies in the descriptions algorithmically. In experiments on an educational data set, we show that LLMs can translate natural-language descriptions into equivalent, syntactically close Nile expressions with high accuracy - allowing to algorithmically provide explanations for incorrect natural-language descriptions. Our experiments also show that while natural-language descriptions can also be translated into regular expressions (but not context-free grammars), the expressions are often not syntactically close and thus not suitable for providing explanations.

cs.FL↗

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↗

arXiv2025

Difficulty Generating Factors for Context-free Language Construction Assignments

Computer science students often struggle with abstract theoretical concepts, particularly in introductory courses on theoretical computer science. One such challenge is understanding context-free languages and their various representations. In this study we investigate factors that influence the difficulty of constructing context-free grammars and pushdown automata for context-free languages. We propose two potential difficulty generating factors targeting how a language is presented to students: representation in natural language and as a verbose set notation. Furthermore, we propose two factors targeting the structure of the given context-free language: nesting of constructs and insertion of multiplicities. We conducted a controlled experiment using within-subject randomization in an interactive learning system, testing the proposed difficulty factors for constructing context-free grammars and pushdown automata. Our results suggest that three of the four factors significantly influence students' objective performance in solving exercises for constructing context-free grammars, while students' perceived difficulties only partly align with the objective performance measures. The findings for pushdown automata tasks differed markedly from those for context-free grammar tasks. Our variations either had negligible effects or, in some cases, even reduced difficulty. Thus, no robust statistical conclusions can be made for pushdown automata tasks. The results lay foundations for learning systems that adaptively choose appropriate exercises for individual students.

cs.CY↗

arXiv2025

Logical Modelling in CS Education: Bridging the Natural Language Gap

An important learning objective for computer science students is to learn how to formalize descriptions of real world scenarios in order to subsequently solve real world challenges using methods and algorithms from formal foundations of computer science. Two key steps when formalizing with logical formalisms are to (a) choose a suitable vocabulary, that is, e.g., which propositional variables or first-order symbols to use, and with which intended meaning, and then to (b) construct actual formal descriptions, i.e. logical formulas over the chosen vocabulary. While (b) is addressed by several educational support systems for formal foundations of computer science, (a) is so far not addressed at all -- likely because it involves specifying the intended meaning of symbols in natural language. We propose a conceptual framework for educational tasks where students choose a vocabulary, including an enriched language for describing solution spaces as well as an NLP-approach for checking student attempts and providing feedback. We implement educational tasks for designing propositional and first-order vocabularies within the Iltis educational system, and report on experiments with data from introductory logic courses for computer science students with > 25.000 data points.

cs.LO↗

arXiv2024

Learning Tree Pattern Transformations

Explaining why and how a tree $t$ structurally differs from another tree $t^\star$ is a question that is encountered throughout computer science, including in understanding tree-structured data such as XML or JSON data. In this article, we explore how to learn explanations for structural differences between pairs of trees from sample data: suppose we are given a set $\{(t_1, t_1^\star),\dots, (t_n, t_n^\star)\}$ of pairs of labelled, ordered trees; is there a small set of rules that explains the structural differences between all pairs $(t_i, t_i^\star)$? This raises two research questions: (i) what is a good notion of "rule" in this context?; and (ii) how can sets of rules explaining a data set be learned algorithmically? We explore these questions from the perspective of database theory by (1) introducing a pattern-based specification language for tree transformations; (2) exploring the computational complexity of variants of the above algorithmic problem, e.g. showing NP-hardness for very restricted variants; and (3) discussing how to solve the problem for data from CS education research using SAT solvers.

cs.LG↗

arXiv2024

Exploring Error Types in Formal Languages Among Students of Upper Secondary Education

Foundations of formal languages, as subfield of theoretical computer science, are part of typical upper secondary education curricula. There is very little research on the potential difficulties that students at this level have with this subject. In this paper, we report on an exploratory study of errors in formal languages among upper secondary education students. We collect the data by posing exercises in an intelligent tutoring system and analyzing student input. Our results suggest a) instances of non-functional understanding of concepts such as the empty word or a grammar as a substitution system; b) strategic problems such as lack of foresight when deriving a word or confounding formal specifications with real-world knowledge on certain aspects; and c) various syntactic problems. These findings can serve as a starting point for a broader understanding of how and why students struggle with this topic.

cs.CY↗

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↗

arXiv2024

Tool-Assisted Learning of Computational Reductions

Computational reductions are an important and powerful concept in computer science. However, they are difficult for many students to grasp. In this paper, we outline a concept for how the learning of reductions can be supported by educational support systems. We present an implementation of the concept within such a system, concrete web-based and interactive learning material for reductions, and report on our experiences using the material in a large introductory course on theoretical computer science.

cs.CY↗

arXiv2024

Detecting and Explaining (In-)equivalence of Context-Free Grammars

We propose a scalable framework for deciding, proving, and explaining (in-)equivalence of context-free grammars. We present an implementation of the framework and evaluate it on large data sets collected within educational support systems. Even though the equivalence problem for context-free languages is undecidable in general, the framework is able to handle a large portion of these datasets. It introduces and combines techniques from several areas, such as an abstract grammar transformation language to identify equivalent grammars as well as sufficiently similar inequivalent grammars, theory-based comparison algorithms for a large class of context-free languages, and a graph-theory-inspired grammar canonization that allows to efficiently identify isomorphic grammars.

cs.FL↗

arXiv2024

Specification and Automatic Verification of Computational Reductions

We are interested in the following validation problem for computational reductions: for algorithmic problems $P$ and $P^\star$, is a given candidate reduction indeed a reduction from $P$ to $P^\star$? Unsurprisingly, this problem is undecidable even for very restricted classes of reductions. This leads to the question: Is there a natural, expressive class of reductions for which the validation problem can be attacked algorithmically? We answer this question positively by introducing an easy-to-use graphical specification mechanism for computational reductions, called cookbook reductions. We show that cookbook reductions are sufficiently expressive to cover many classical graph reductions and expressive enough so that SAT remains NP-complete (in the presence of a linear order). Surprisingly, the validation problem is decidable for natural and expressive subclasses of cookbook reductions.

cs.CC↗

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↗

arXiv2022

The Regular Languages of First-Order Logic with One Alternation

The regular languages with a neutral letter expressible in first-order logic with one alternation are characterized. Specifically, it is shown that if an arbitrary $Σ_2$ formula defines a regular language with a neutral letter, then there is an equivalent $Σ_2$ formula that only uses the order predicate. This shows that the so-called Central Conjecture of Straubing holds for $Σ_2$ over languages with a neutral letter, the first progress on the Conjecture in more than 20 years. To show the characterization, lower bounds against polynomial-size depth-3 Boolean circuits with constant top fan-in are developed. The heart of the combinatorial argument resides in studying how positions within a language are determined from one another, a technique of independent interest.

cs.LO↗

arXiv2021

Work-sensitive Dynamic Complexity of Formal Languages

Which amount of parallel resources is needed for updating a query result after changing an input? In this work we study the amount of work required for dynamically answering membership and range queries for formal languages in parallel constant time with polynomially many processors. As a prerequisite, we propose a framework for specifying dynamic, parallel, constant-time programs that require small amounts of work. This framework is based on the dynamic descriptive complexity framework by Patnaik and Immerman.

cs.LO↗

arXiv2021

Register Automata with Extrema Constraints, and an Application to Two-Variable Logic

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.

cs.LO↗

arXiv2020

Dynamic complexity of Reachability: How many changes can we handle?

In 2015, it was shown that reachability for arbitrary directed graphs can be updated by first-order formulas after inserting or deleting single edges. Later, in 2018, this was extended for changes of size $\frac{\log n}{\log \log n}$, where $n$ is the size of the graph. Changes of polylogarithmic size can be handled when also majority quantifiers may be used. In this paper we extend these results by showing that, for changes of polylogarithmic size, first-order update formulas suffice for maintaining (1) undirected reachability, and (2) directed reachability under insertions. For classes of directed graphs for which efficient parallel algorithms can compute non-zero circulation weights, reachability can be maintained with update formulas that may use "modulo 2" quantifiers under changes of polylogarithmic size. Examples for these classes include the class of planar graphs and graphs with bounded treewidth. The latter is shown here. As the logics we consider cannot maintain reachability under changes of larger sizes, our results are optimal with respect to the size of the changes.

cs.LO↗