February 2025
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4 Reads
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February 2025
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4 Reads
December 2024
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9 Reads
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1 Citation
November 2024
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6 Reads
October 2024
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4 Reads
Explaining why and how a tree t structurally differs from another tree 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 of pairs of labelled, ordered trees; is there a small set of rules that explains the structural differences between all pairs ? 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 learnt 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.
September 2024
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17 Reads
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.
July 2024
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2 Reads
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.
July 2024
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10 Reads
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.
July 2024
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3 Reads
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.
July 2024
We are interested in the following validation problem for computational reductions: for algorithmic problems P and , is a given candidate reduction indeed a reduction from P to ? 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.
March 2023
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14 Reads
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2 Citations
... It is well-known 4 that for every NC-circuit of depth f (n) 3 Other papers write DynFO for the class that uses FO update formulas without a priori access to the arithmetic relations ≤, +, × and DynFO(≤, +, ×) for the class that uses FO(≤, +, ×) update formulas. If changes only affect single tuples, there is no difference for most interesting queries, see [9,Proposition 7]. For changes that affect sets of tuples of non-constant size, all DynFO maintainability results use FO(≤, +, ×) update formulas, as FO update formulas without arithmetic are not strong enough to maintain interesting queries. ...
August 2018
Journal of the ACM
... Besides supporting students, these systems also have great potential for collecting educational data to gain insights into students' thinking. For example, the Iltis system has been used to detect common errors in modeling with formulas [23]. ...
March 2023
... The prefix contains only two blocks of alternating quantifiers, beginning with an existential quantifier: thus the language is in Σ 2 [<]. We note that this complexity measure is conjectured to be closely related to the minimal depth of an equivalent Boolean circuit and that depth is tied to the speed at which the circuit can be evaluated [32] -this conjecture is known to hold up to Σ 2 [<] [4]. It is thus of crucial importance to find what is the minimal number of alternations required to define a given language. ...
August 2022
... The proof of non-regularity of Double is easy (see Appendix C). One could also easily show that Double cannot be recognized by other existing models in the literature of formal language theory over infinite alphabets, e.g., register automata [4,9,24,36,41], variable/parametric automata [16,19,23], and data automata variants [5,17]. For example, for register automata over (Q; <) (see the book [4]), one could use the result therein that data sequences accepted by such an automaton are closed under any order-preserving map of the elements in the sequence (e.g., if 1, 2, 3 is accepted, then so is 10,11,20), which is not satisfied by Double. ...
March 2022
Logical Methods in Computer Science
... It is yet to be seen whether this could be useful for real-world systems, however, some recent work has looked at applying dynamic complexity. Schmidt, Schwentick, Tantau, Vortmeier and Zeume [103] studied the amount of parallel work needed to maintain an answer to certain questions (such as range queries) over words that are subject to updates. Chapter 6. ...
March 2021
Lecture Notes in Computer Science
... We introduce some concepts and notation that we need throughout the paper. See also [21] for an overview of Dynamic Complexity. We assume familiarity with first-order logic FO, and refer to [18] for basics of Finite Model Theory. ...
December 2020
ACM SIGMOD Record
... We now shortly recapitulate the dynamic complexity framework as introduced by Patnaik and Immerman [PI97], and refer to Reference [SZ16] for details. ...
May 2016
ACM SIGLOG News
... However, we demonstrate that this problem can be effectively reduced to finite KBSat for ZIQ, making the finite KBSat the main problem to study. We apply our methods to derive new results for extensions of ALC with transitive closure of roles (Jung, Lutz, and Zeume 2020) and to lift some known results about finite CQ entailment for various DLs to the setting of local queries. ...
July 2020
... This is described in Section 4. Decidability then follows from the fact that the emptiness problem for parity automata is decidable [Rab72]. This article is the long version of [TZ20]. It in particular provides full proofs for all results. ...
July 2020
... Además, facilita la lectura, escritura y Prácticas docentes de aula en la enseñanza del pensamiento computacional en escuelas medias oficiales y particulares de la región metropolitana de la Ciudad de Panamá REVISTA ANUAL, ACCIÓN Y REFLEXIÓN EDUCATIVA, N° 46 Enero, 2021 ISSN L 2644-3775 212 comprensión de especificaciones formales y su análisis (Mossakowski, 2010). Por otro lado, modelar escenarios utilizando formalismos lógicos e inferir nuevos conocimientos son habilidades importantes en el campo de la enseñanza de la informática (Geck et al., 2018). Por lo tanto, el aprendizaje de formalismos lógicos y, en particular, el modelado lógico es de suma importancia para los estudiantes de informática. ...
July 2019