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  • 1.
    Bensch, Suna
    et al.
    Umeå University, Faculty of Science and Technology, Department of Computing Science.
    Drewes, Frank
    Umeå University, Faculty of Science and Technology, Department of Computing Science.
    Jürgensen, Helmut
    Department of Computer Science, Western University, London, Canada.
    van der Merwe, Brink
    Department of Computer Science, Stellenbosch University, South Africa.
    Graph transformation for incremental natural language analysis2014In: Theoretical Computer Science, ISSN 0304-3975, E-ISSN 1879-2294, Vol. 531, p. 1-25Article in journal (Refereed)
    Abstract [en]

    Millstream systems have been proposed as a non-hierarchical method for modelling natural language. Millstream configurations represent and connect multiple structural aspects of sentences. We present a method by which the Millstream configurations corresponding to a sentence are constructed. The construction is incremental, that is, it proceeds as the sentence is being read and is complete when the end of the sentence is reached. It is based on graph transformations and a lexicon which associates words with graph transformation rules that implement the incremental construction process.

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  • 2.
    Berglund, Martin
    et al.
    Department of Information Science and Centre for AI Research, University of Stellenbosch, Matieland, South Africa.
    Bester, Willem
    Division of Computer Science, University of Stellenbosch, Matieland, South Africa.
    van der Merwe, Brink
    Division of Computer Science, University of Stellenbosch, Matieland, South Africa.
    Formalising and implementing Boost POSIX regular expression matching2021In: Theoretical Computer Science, ISSN 0304-3975, E-ISSN 1879-2294, Vol. 857, p. 147-165Article in journal (Refereed)
    Abstract [en]

    Whereas Perl-compatible regular expression matchers typically exhibit some variation of leftmost-greedy semantics, those conforming to the posix standard are prescribed leftmost-longest semantics. However, the posix standard leaves some room for interpretation, and Fowler and Kuklewicz have done experimental work to confirm differences between various posix matchers. The Boost library has an interesting take on the posix standard, where it maximises the leftmost match not with respect to subexpressions of the regular expression pattern, but rather, with respect to capturing groups. In our work, we provide the first formalisation of Boost semantics, analyze the complexity of regular expression matching when using Boost semantics, and provide efficient algorithms for both online and multipass matching.

  • 3.
    Berglund, Martin
    et al.
    Umeå University, Faculty of Science and Technology, Department of Computing Science.
    Björklund, Henrik
    Umeå University, Faculty of Science and Technology, Department of Computing Science.
    Björklund, Johanna
    Umeå University, Faculty of Science and Technology, Department of Computing Science.
    Shuffled languages: representation and recognition2013In: Theoretical Computer Science, ISSN 0304-3975, E-ISSN 1879-2294, Vol. 489-490, p. 1-20Article in journal (Refereed)
    Abstract [en]

    Language models that use interleaving, or shuffle, operators have applications in various areas of computer science, including system verification, plan recognition, and natural language processing. We study the complexity of the membership problem for such models, in other words, how difficult it is to determine if a string belongs to a language or not. In particular, we investigate how interleaving can be introduced into models that capture the context-free languages.

  • 4.
    Berglund, Martin
    et al.
    Umeå University, Faculty of Science and Technology, Department of Computing Science.
    van der Merwe, Brink
    On the semantics of regular expression parsing in the wild2017In: Theoretical Computer Science, ISSN 0304-3975, E-ISSN 1879-2294, Vol. 679, p. 69-82Article in journal (Refereed)
    Abstract [en]

    We introduce prioritized transducers to formalize capturing groups in regular expression matching in a way that permits straightforward modeling of capturing in Java's 1 regular expression library. The broader questions of parsing semantics and performance are also considered. In addition, the complexity of deciding equivalence of regular expressions with capturing groups is investigated.

  • 5.
    Berglund, Martin
    et al.
    Centre for AI Research, CSIR, Department of Information Science, Stellenbosch University, South Africa.
    van der Merwe, Brink
    Department of Computer Science, Stellenbosch University, South Africa.
    Re-examining regular expressions with backreferences2023In: Theoretical Computer Science, ISSN 0304-3975, E-ISSN 1879-2294, Vol. 940, p. 66-80Article in journal (Refereed)
    Abstract [en]

    Most modern regular expression matching libraries (one of the rare exceptions being Google's RE2) allow backreferences, operations which bind a substring to a variable, allowing it to be matched again verbatim. However, both real-world implementations and definitions in the literature use different syntactic restrictions and have differences in the semantics of the matching of backreferences. Our aim is to compare these various flavors by considering the classes of formal languages that each can describe, establishing, as a result, a hierarchy of language classes. Beyond the hierarchy itself, some complexity results are given, and as part of the effort on comparing language classes new pumping lemmas are established, old classes are extended to new ones, and several incidental results on the nature of these language classes are given.

  • 6.
    Björklund, Henrik
    et al.
    Umeå University, Faculty of Science and Technology, Department of Computing Science.
    Björklund, Johanna
    Umeå University, Faculty of Science and Technology, Department of Computing Science.
    Zechner, Niklas
    Umeå University, Faculty of Science and Technology, Department of Computing Science.
    Compression of finite-state automata through failure transitions2014In: Theoretical Computer Science, ISSN 0304-3975, E-ISSN 1879-2294, Vol. 557, p. 87-100Article in journal (Refereed)
    Abstract [en]

    Several linear-time algorithms for automata-based pattern matching rely on failure transitions for efficient back-tracking. Like epsilon transitions, failure transition do not consume input symbols, but unlike them, they may only be taken when no other transition is applicable. At a semantic level, this conveniently models catch-all clauses and allows for compact language representation.

    This work investigates the transition-reduction problem for deterministic finite-state automata (DFA). The input is a DFA A and an integer k. The question is whether k or more transitions can be saved by replacing regular transitions with failure transitions. We show that while the problem is NP-complete, there are approximation techniques and heuristics that mitigate the computational complexity. We conclude by demonstrating the computational difficulty of two related minimisation problems, thereby cancelling the ongoing search for efficient algorithms.

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  • 7.
    Björklund, Henrik
    et al.
    Umeå University, Faculty of Science and Technology, Department of Computing Science.
    Schwentick, Thomas
    On notions of regularity for data languages2010In: Theoretical Computer Science, ISSN 0304-3975, E-ISSN 1879-2294, Vol. 411, no 4-5, p. 702-715Article in journal (Refereed)
    Abstract [en]

    With motivation from considerations in XML database theory and model checking, data strings have been introduced as an extension of finite alphabet strings which carry, at each position, a symbol and a data value from an infinite domain. Previous work has shown that it is difficult to come up with an expressive yet decidable automaton model for data languages. Recently, such a model, data automata, was introduced. This paper introduces a simpler but equivalent model and investigates its expressive power, algorithmic and closure properties, and some extensions.

  • 8.
    Björklund, Johanna
    et al.
    Umeå University, Faculty of Science and Technology, Department of Computing Science.
    Cohen, Shay B.
    University of Edinburgh, United Kingdom.
    Drewes, Frank
    Umeå University, Faculty of Science and Technology, Department of Computing Science.
    Satta, Giorgio
    University of Padova, Italy.
    Bottom-up unranked tree-to-graph transducers for translation into semantic graphs2021In: Theoretical Computer Science, ISSN 0304-3975, E-ISSN 1879-2294, Vol. 870, p. 3-28Article in journal (Refereed)
    Abstract [en]

    We develop a finite-state transducer for translating unranked trees into general graphs. This work is motivated by recent progress in semantic parsing for natural language, where sentences are first mapped into tree-shaped syntactic representations, and then these trees are translated into graph semantic representations. We investigate formal properties of our tree-to-graph transducers and develop a polynomial time algorithm for translating a weighted language of input trees into a packed representation, from which best-score graphs can be efficiently recovered.

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  • 9.
    Björklund, Johanna
    et al.
    Umeå University, Faculty of Science and Technology, Department of Computing Science.
    Drewes, Frank
    Umeå University, Faculty of Science and Technology, Department of Computing Science.
    Jonsson, Anna
    Umeå University, Faculty of Science and Technology, Department of Computing Science.
    Finding the N Best Vertices in an Infinite Weighted Hypergraph2017In: Theoretical Computer Science, ISSN 0304-3975, E-ISSN 1879-2294, Vol. 682, p. 78p. 30-41Article in journal (Refereed)
    Abstract [en]

    We propose an algorithm for computing the N best vertices in a weighted acyclic hypergraph over a nice semiring. A semiring is nice if it is finitely-generated, idempotent, and has 1 as its minimal element. We then apply the algorithm to the problem of computing the N best trees with respect to a weighted tree automaton, and complement theoretical correctness and complexity arguments with experimental data. The algorithm has several practical applications in natural language processing, for example, to derive the N most likely parse trees with respect to a probabilistic context-free grammar. 

  • 10.
    Björklund, Johanna
    et al.
    Umeå University, Faculty of Science and Technology, Department of Computing Science.
    Öhman, Lars-Daniel
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Simulation relations for pattern matching in directed graphs2013In: Theoretical Computer Science, ISSN 0304-3975, E-ISSN 1879-2294, Vol. 485, p. 1-15Article in journal (Refereed)
    Abstract [en]

    We consider the problem of finding the occurrences of a pattern tree t in a directed graph g, and propose two algorithms, one for preprocessing and one for searching for t in g. It is assumed that the object graph itself is large and static, and that the pattern tree is small and frequently updated. To model varying abstraction levels in the data, we work with partially ordered alphabets and compute simulation relations rather than equivalence relations. In particular, vertices and edges are labelled with elements from a pair of preorders instead of unstructured alphabets. Under the above assumptions, we obtain a search algorithm that runs in time O(height (t) . vertical bar t vertical bar . vertical bar(V-g(+/-)t/R-g(+/-)t vertical bar(2)) where vertical bar (V-g(+/-)t/R-g(+/-)t)vertical bar is the number of equivalence classes in the coarsest simulation relation R-g(+/-)t on the graph g((+/-))t, the disjoint union of g and t. This means that the size of the object graph only affects the running time of the search algorithm indirectly, because of the groundwork done by the preprocessing routine in time O(k . vertical bar g vertical bar . vertical bar(V-g/R-g)vertical bar(2)), where vertical bar(V-g/R-g) is the number of equivalence classes in the coarsest simulation relation R-g on g, taking k = vertical bar V-g vertical bar(2) in the general case and k = height (g) if g is acyclic.

  • 11.
    Drewes, Frank
    Umeå University, Faculty of Science and Technology, Department of Computing Science.
    Preface2017In: Theoretical Computer Science, ISSN 0304-3975, E-ISSN 1879-2294, Vol. 679, p. 1-1Article in journal (Other academic)
  • 12.
    Drewes, Frank
    et al.
    Umeå University, Faculty of Science and Technology, Department of Computing Science.
    Janssens, Dirk
    University of Antwerp.
    Hoffmann, Berthold
    University of Bremen.
    Minas, Mark
    University of the German Armed Forces Munich.
    Adaptive Star grammars and their languages2010In: Theoretical Computer Science, ISSN 0304-3975, E-ISSN 1879-2294, Vol. 411, no 34-36, p. 3090-3109Article in journal (Refereed)
  • 13.
    Drewes, Frank
    et al.
    Umeå University, Faculty of Science and Technology, Department of Computing Science.
    Mörbitz, Richard
    Technische Universität Dresden, Germany.
    Vogler, Heiko
    Technische Universität Dresden, Germany.
    Hybrid tree automata and the yield theorem for constituent tree automata2023In: Theoretical Computer Science, ISSN 0304-3975, E-ISSN 1879-2294, Vol. 979, article id 114185Article in journal (Refereed)
    Abstract [en]

    We introduce an automaton model for recognizing sets of hybrid trees, the hybrid tree automaton (HTA). Special cases of hybrid trees are constituent trees and dependency trees, as they occur in natural language processing. This includes the cases of discontinuous constituent trees and non-projective dependency trees. In general, a hybrid tree is a tree over a ranked alphabet in which a symbol can additionally be equipped with a natural number, called index; in a hybrid tree, each index occurs at most once. The yield of a hybrid tree is a sequence of strings over those symbols which occur in an indexed form; the corresponding indices determine the order within these strings; the borders between two consecutive strings are determined by the gaps in the sequence of indices. As a special case of HTA, we define constituent tree automata (CTA) which recognize sets of constituent trees. We introduce the notion of CTA-inductively recognizable and we show that the set of yields of a CTA-inductively recognizable set of constituent trees is an LCFRS language, and vice versa.

  • 14.
    Jäger, Gerold
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Drewes, Frank
    Umeå University, Faculty of Science and Technology, Department of Computing Science.
    The Metric Dimension of Z(n) x Z(n) x Z(n) is [3n/2]2020In: Theoretical Computer Science, ISSN 0304-3975, E-ISSN 1879-2294, Vol. 806, p. 78p. 344-362Article in journal (Refereed)
    Abstract [en]

    In this work we determine the metric dimension of Zn × Zn × Zn as ⌊3n/2⌋ for all n ≥ 2. We prove this result by investigating a variant of Mastermind.

    Mastermind is a famous two-player game that has attracted much attention in the literature in recent years. In particular we consider the static (also called non-adaptive) black-peg variant of Mastermind. The game is played by a codemaker and a codebreaker. Given c colors and p pegs, the principal rule is that the codemaker has to choose a secret by assigning colors to the pegs, i.e., the secret is a p-tuple of colors, and the codebreaker asks a number of questions all at once. Like the secret, a question is a p-tuple of colors chosen from the c available colors. The codemaker then answers all of those questions by telling the codebreaker how many pegs in each question are correctly colored. The goal is to find the minimal number of questions that allows the codebreaker to determine the secret from the received answers. We present such a strategy for this game for p = 3 pegs and an arbitrary number c ≥ 2 of colors using ⌊3c/2⌋ + 1 questions, which we prove to be both feasible and optimal.

    The minimal number of questions required for p pegs and c colors is easily seen to be equal to the metric dimension of Zcp plus 1 which proves our main result.

  • 15.
    Jäger, Gerold
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Peczarski, Marcin
    Bounding memory for Mastermind might not make it harder2015In: Theoretical Computer Science, ISSN 0304-3975, E-ISSN 1879-2294, Vol. 596, p. 55-66Article in journal (Refereed)
  • 16. Trávníček, Jan
    et al.
    Janoušek, Jan
    Melichar, Bořivoj
    Cleophas, Loek
    Umeå University, Faculty of Science and Technology, Department of Computing Science. FASTAR Research Group, Department of Information Science, Stellenbosch University, Matieland, South Africa.
    On modification of Boyer-Moore-horspool's algorithm for tree pattern matching in linearised trees2020In: Theoretical Computer Science, ISSN 0304-3975, E-ISSN 1879-2294, Vol. 830-831, p. 60-90Article in journal (Refereed)
    Abstract [en]

    Tree pattern matching on ordered trees is an important problem in Computer Science. Ordered trees can be represented as strings with additional properties via various linearisations. We present a backward tree pattern matching algorithm for ordered trees for various linear representations of trees and tree patterns. The algorithm adaptations find all occurrences of a single given tree pattern which match an input tree regardless of the chosen linearisation. The algorithms preserve the properties and advantages of standard backward string pattern matching using Boyer-Moore-Horspool's bad character shift heuristics. The number of symbol comparisons in the backward tree pattern matching can be sublinear in the size of the input tree. As in the case of the string version of Boyer-Moore-Horspool's matching algorithm, the size of the bad character shift table used by the algorithm is linear in the size of the alphabet. We compare the algorithm adaptations with the algorithm using originally chosen linear representation and with the best performing previously existing algorithms based on (non-linearised) tree pattern matching using finite tree automata or stringpath matchers. We show that the presented backward tree pattern matching algorithms outperform the non-linearising ones for single pattern matching and they perform among themselves comparably.

  • 17.
    Turkensteen, Marcel
    et al.
    Department of Economics and Business Economics, School of Business and Social Sciences, Aarhus University, Aarhus, Denmark.
    Jäger, Gerold
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Efficient computation of tolerances in the sensitivity analysis of combinatorial bottleneck problems2022In: Theoretical Computer Science, ISSN 0304-3975, E-ISSN 1879-2294, Vol. 937, p. 1-21Article in journal (Refereed)
    Abstract [en]

    This paper considers combinatorial optimization problems with an objective of type bottleneck, so the objective is to minimize the maximum cost among all elements in a feasible solution. For these problems, the sensitivity of an optimal solution to changes in parameters has received much less attention in existing studies than the computation of an optimal solution. This paper introduces methods for computing upper and lower tolerances which measure the amount of cost change needed in an element inside and outside an optimal solution, respectively, before that solution becomes non-optimal. Our main contribution is the development of efficient computation methods for bottleneck versions of the Linear Assignment Problem and the Minimum Spanning Tree Problem.

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