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  • 51.
    Jonsson, Peter
    et al.
    Linköping University, Department of Computer and Information Science, Software and Systems. Linköping University, Faculty of Science & Engineering.
    Thapper, Johan
    Univ Paris Est Marne la Vallee, France.
    Tractability conditions for numeric CSPs2018In: Theoretical Computer Science, ISSN 0304-3975, E-ISSN 1879-2294, Vol. 715, p. 21-34Article in journal (Refereed)
    Abstract [en]

    The computational complexity of the constraint satisfaction problem (CSP) with semilinear relations over the reals has gained recent attraction. As a result, its complexity is known for all finite sets of semilinear relations containing the relation R+ = {(x, y, z) is an element of R-3 vertical bar x + y = z}. We consider larger and more expressive classes of relations such as semialgebraic and o-minimal relations. We present a general result for characterising computationally hard fragments and, under certain side conditions, this result implies that polynomial-time solvable fragments are only to be found within two limited families of sets of relations. In the setting of semialgebraic relation, our result takes on a simplified form and we provide a full complexity classification for constraint languages that consist of algebraic varieties. Full classifications like the one obtained here for algebraic varieties or the one for semilinear relations appear to be rare and we discuss several barriers for obtaining further such results. These barriers have strong connections with well-known open problems concerning the complexity of various restrictions of convex programming. (c) 2018 Elsevier B.V. All rights reserved.

  • 52.
    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.

  • 53.
    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)
  • 54.
    Kostitsyna, Irina
    et al.
    Eindhoven University of Technology, Netherlands.
    Loffler, Maarten
    University of Utrecht, Netherlands.
    Polishchuk, Valentin
    Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, Faculty of Science & Engineering.
    Optimizing airspace closure with respect to politicians egos2015In: Theoretical Computer Science, ISSN 0304-3975, E-ISSN 1879-2294, Vol. 586, p. 161-175Article in journal (Refereed)
    Abstract [en]

    When a president is landing at a busy airport, the airspace around the airport closes for commercial traffic. We show how to schedule the presidential squadron so as to minimize its impact on scheduled civilian flights; to obtain an efficient solution we use a "rainbow" algorithm recoloring aircraft on the fly as they are stored in a special type of forest. We also give a data structure to answer the following query efficiently: Given the presidents ego (the requested duration of airspace closure), when would be the optimal time to close the airspace? Finally, we study the dual problem: Given the time when the airspace closure must start, what is the longest ego that can be tolerated without sacrificing the general traffic? We solve the problem by drawing a Christmas tree in a delay diagram; the tree allows one to solve also the query version of the problem. (C) 2015 Elsevier B.V. All rights reserved.

  • 55.
    Malmberg, Filip
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Centre for Image Analysis. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computerized Image Analysis and Human-Computer Interaction.
    Lindblad, Joakim
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Centre for Image Analysis.
    Sladoje, Natasa
    Faculty of Technical Sciences, University of Novi Sad.
    Nyström, Ingela
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Centre for Image Analysis. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computerized Image Analysis and Human-Computer Interaction.
    A Graph-based Framework for Sub-pixel Image Segmentation2011In: Theoretical Computer Science, ISSN 0304-3975, E-ISSN 1879-2294, Vol. 412, no 15, p. 1338-1349Article in journal (Refereed)
    Abstract [en]

    Many image segmentation methods utilize graph structures for representing images, where the flexibility and generality of the abstract structure is beneficial. By using a fuzzy object representation, i.e., allowing partial belongingness of elements to image objects, the unavoidable loss of information when representing continuous structures by finite sets is significantly reduced,enabling feature estimates with sub-pixel precision.This work presents a framework for object representation based on fuzzysegmented graphs. Interpreting the edges as one-dimensional paths betweenthe vertices of a graph, we extend the notion of a graph cut to that of a located cut, i.e., a cut with sub-edge precision. We describe a method for computing a located cut from a fuzzy segmentation of graph vertices. Further,the notion of vertex coverage segmentation is proposed as a graph theoretic equivalent to pixel coverage segmentations and a method for computing such a segmentation from a located cut is given. Utilizing the proposed framework,we demonstrate improved precision of area measurements of synthetic two-dimensional objects. We emphasize that although the experiments presented here are performed on two-dimensional images, the proposed framework is defined for general graphs and thus applicable to images of any dimension.

  • 56. Milner, Robin
    et al.
    Parrow, Joachim
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Computer Systems. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computing Science.
    Walker, David
    Modal Logics for Mobile Processes1993In: Theoretical Computer Science, ISSN 0304-3975, E-ISSN 1879-2294, Vol. 114, no 1, p. 149-171Article in journal (Refereed)
    Abstract [en]

    In process algebras, bisimulation equivalence is typically defined directly in terms of the operational rules of action; it also has an alternative characterization in terms of a simple modal logic (sometimes called Hennessy-Milner logic). This paper first defines two forms of bisimulation equivalence for the π-calculus, a process algebra which allows dynamic reconfiguration among processes; it then explores a family of possible logics, with different modal operators. It is proven that two of these logics characterize the two bisimulation equivalences. Also, the relative expressive power of all the logics is exhibited as a lattice. The results are applicable to most value-passing process algebras.

  • 57.
    Moggi, E.
    et al.
    DIBRIS, Genova Univ., v. Dodecaneso 35, Genova, 16146, Italy.
    Farjudian, A.
    University of Nottingham Ningbo, China.
    Duracz, Adam
    Rice University, Houston, TX, United States.
    Taha, Walid
    Halmstad University, School of Information Technology, Halmstad Embedded and Intelligent Systems Research (EIS), Centre for Research on Embedded Systems (CERES).
    Safe & robust reachability analysis of hybrid systems2018In: Theoretical Computer Science, ISSN 0304-3975, E-ISSN 1879-2294, Vol. 747, p. 75-99Article in journal (Refereed)
    Abstract [en]

    Hybrid systems—more precisely, their mathematical models—can exhibit behaviors, like Zeno behaviors, that are absent in purely discrete or purely continuous systems. First, we observe that, in this context, the usual definition of reachability—namely, the reflexive and transitive closure of a transition relation—can be unsafe, i.e., it may compute a proper subset of the set of states reachable in finite time from a set of initial states. Therefore, we propose safe reachability, which always computes a superset of the set of reachable states. Second, in safety analysis of hybrid and continuous systems, it is important to ensure that a reachability analysis is also robust w.r.t. small perturbations to the set of initial states and to the system itself, since discrepancies between a system and its mathematical models are unavoidable. We show that, under certain conditions, the best Scott continuous approximation of an analysis A is also its best robust approximation. Finally, we exemplify the gap between the set of reachable states and the supersets computed by safe reachability and its best robust approximation. © 2018 The Authors

  • 58.
    Mousavi, Mohammad Reza
    et al.
    Department of Computer Science, Eindhoven University of Technology (TU/e), P.O. Box 513, NL-5600 MB Eindhoven, Netherlands.
    Reniers, M. A.
    Department of Computer Science, Eindhoven University of Technology (TU/e), P.O. Box 513, NL-5600 MB Eindhoven, Netherlands.
    Groote, J. F.
    Department of Computer Science, Eindhoven University of Technology (TU/e), P.O. Box 513, NL-5600 MB Eindhoven, Netherlands.
    SOS formats and meta-theory: 20 years after2007In: Theoretical Computer Science, ISSN 0304-3975, E-ISSN 1879-2294, Vol. 373, p. 238-272Article in journal (Refereed)
    Abstract [en]

    In 1981 Structural Operational Semantics (SOS) was introduced as a systematic way to define operational semantics of programming languages by a set of rules of a certain shape [G.D. Plotkin, A structural approach to operational semantics, Technical Report DAIMI FN-19, Computer Science Department, Aarhus University, Aarhus, Denmark, September 1981]. Subsequently, the format of SOS rules became the object of study. Using so-called Transition System Specifications (TSS's) several authors syntactically restricted the format of rules and showed several useful properties about the semantics induced by any TSS adhering to the format. This has resulted in a line of research proposing several syntactical rule formats and associated meta-theorems. Properties that are guaranteed by such rule formats range from well-definedness of the operational semantics and compositionality of behavioral equivalences to security-, time- and probability-related issues. In this paper, we provide an overview of SOS rule formats and meta-theorems formulated around them. © 2007 Elsevier Ltd. All rights reserved.

  • 59. Nagy, Benedek
    et al.
    Strand, Robin
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Centre for Image Analysis. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computerized Image Analysis and Human-Computer Interaction.
    Approximating Euclidean circles by neighbourhood sequences in a hexagonal grid2011In: Theoretical Computer Science, ISSN 0304-3975, E-ISSN 1879-2294, Vol. 412, no 15, p. 1364-1377Article in journal (Refereed)
  • 60.
    Nilsson, Ulf
    Linköping University, Department of Computer and Information Science, TCSLAB - Theoretical Computer Science Laboratory. Linköping University, The Institute of Technology.
    Abstract Interpretation: A Kind of Magic1995In: Theoretical Computer Science, ISSN 0304-3975, E-ISSN 1879-2294, Vol. 142, no 1, p. 125-138Article in journal (Refereed)
    Abstract [en]

    Magic sets and, more recently, magic templates have been used in the field of deductive databases to facilitate efficient bottom-up evaluation of database queries. Roughly speaking a top-down computation of a definite logic program is simulated by first transforming the program and then executing the new program bottom-up. In this paper we give a new and very simple proof that this approach is equivalent to the collecting interpretation of the abstract interpretation framework for logic programs of Mellish. As a side-effect we are also able to show that “bottom-up” abstract interpretation based on the magic templates transformation is equally powerful as Mellish's abstract interpretation framework, but less powerful than other (more precise) abstract interpretation frameworks.

  • 61.
    Parrow, Joachim
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Computer Systems. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computing Science.
    Submodule Construction as Equation Solving in CCS1989In: Theoretical Computer Science, ISSN 0304-3975, E-ISSN 1879-2294, Vol. 68, no 2, p. 175-202Article in journal (Refereed)
  • 62.
    Strand, Robin
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Centre for Image Analysis. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computerized Image Analysis and Human-Computer Interaction.
    Nagy, Benedek
    Borgefors, Gunilla
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Centre for Image Analysis. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computerized Image Analysis and Human-Computer Interaction.
    Digital distance functions on three-dimensional grids2011In: Theoretical Computer Science, ISSN 0304-3975, E-ISSN 1879-2294, Vol. 412, no 15, p. 1350-1363Article in journal (Refereed)
  • 63.
    Strand, Robin
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Visual Information and Interaction. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computerized Image Analysis and Human-Computer Interaction.
    Normand, Nicolas
    Distance transform computation for digital distance functions2012In: Theoretical Computer Science, ISSN 0304-3975, E-ISSN 1879-2294, Vol. 448, p. 80-93Article in journal (Refereed)
    Abstract [en]

    In image processing, the distance transform (DT), in which each object grid point is assigned the distance to the closest background grid point, is a powerful and often used tool. In this paper, distance functions defined as minimal cost-paths are used and a number of algorithms that can be used to compute the DT are presented. We give proofs of the correctness of the algorithms.

  • 64.
    Szalas, Andrzej
    University of Warsaw.
    A Complete Axiomatic Characterization of First-Order Temporal Logic of Linear Time1987In: Theoretical Computer Science, ISSN 0304-3975, E-ISSN 1879-2294, Vol. 54, no 2-3, p. 199-214Article in journal (Refereed)
    Abstract [en]

    As shown in (Szalas, 1986, 1986, 1987) there is no finitistic and complete axiomatization of First-Order Temporal Logic of linear and discrete time. In this paper we give an infinitary proof system for the logic. We prove that the proof system is sound and complete. We also show that any syntactically consistent temporal theory has a model. As a corollary we obtain that the Downward Theorem of Skolem, Lowenheim and Tarski holds in the case of considered logic.

  • 65.
    Szalas, Andrzej
    Institute of Informatics, University of Warsaw, Poland.
    Concerning the Semantic Consequence Relation in First-Order Temporal Logic1986In: Theoretical Computer Science, ISSN 0304-3975, E-ISSN 1879-2294, Vol. 47, no 3, p. 329-334Article in journal (Refereed)
    Abstract [en]

    In this paper we consider the first-order temporal logic with linear and discrete time. We prove that the set of tautologies of this logic is not arithmetical (i.e., it is neither Σ0n nor Π0n for any natural number n). Thus we show that there is no finitistic and complete axiomatization of the considered logic.

  • 66.
    Szalas, Andrzej
    University of Warsaw.
    On Strictly Arithmetical Completeness in Logics of Programs1991In: Theoretical Computer Science, ISSN 0304-3975, E-ISSN 1879-2294, Vol. 79, no 2, p. 341-355Article in journal (Refereed)
    Abstract [en]

    We introduce and discuss a notion of strictly arithmetical completeness related to relative completeness of Cook (1978) and arithmetical completeness of Harel (1978). We present a powerful technique of obtaining strictly arithmetical axiomatizations of logics of programs. Given a model-theoretic semantics of a logic and a set of formulae defining (in a metalanguage) its nonclassical connectives, we automatically derive strictly arithmetically complete and sound proof systems for this logic. As examples of application of the technique we obtain new axiomatizations of algorithmic logic, (concurrent) dynamic logic and temporal logic.

  • 67.
    Szalas, Andrzej
    et al.
    Institute of Informatics, Warsaw University.
    Holenderski, Leszek
    Institute of Informatics, Warsaw University.
    Incompleteness of First-Order Temporal Logic with Until1988In: Theoretical Computer Science, ISSN 0304-3975, E-ISSN 1879-2294, Vol. 57, no 2-3, p. 317-325Article in journal (Refereed)
    Abstract [en]

    The results presented in this paper concern the axiomatizability problem of first-order temporal logic with linear and discrete time. We show that the logic is incomplete, i.e., it cannot be provided with a finitistic and complete proof system. We show two incompleteness theorems. Although the first one is weaker (it assumes some first-order signature), we decided to present it, for its proof is much simpler and contains an interesting fact that finite sets are characterizable by means of temporal formulas. The second theorem shows that the logic is incomplete independently of any particular signature.

  • 68.
    Taha, Walid
    et al.
    Dept. of Comp. Sci. and Engineering, Oregon Graduate Institute, P.O. Box 91000, Portland, OR 97291, United States.
    Sheard, Tim
    Dept. of Comp. Sci. and Engineering, Oregon Graduate Institute, P.O. Box 91000, Portland, OR 97291, United States.
    MetaML and multi-stage programming with explicit annotations2000In: Theoretical Computer Science, ISSN 0304-3975, E-ISSN 1879-2294, Vol. 248, no 1-2, p. 211-242Article in journal (Refereed)
    Abstract [en]

    We introduce MetaML, a practically motivated, statically typed multi-stage programming language. MetaML is a “real” language. We have built an implementation and used it to solve multi-stage problems. MetaML allows the programmer to construct, combine, and execute code fragments in a type-safe manner. Code fragments can contain free variables, but they obey the static-scoping principle. MetaML performs type-checking for all stages once and for all before the execution of the first stage. Certain anomalies with our first MetaML implementation led us to formalize an illustrative subset of the MetaML implementation. We present both a big-step semantics and type system for this subset, and prove the type system's soundness with respect to a big-step semantics. From a software engineering point of view, this means that generators written in the MetaML subset never generate unsafe programs. A type system and semantics for full MetaML is still ongoing work. We argue that multi-stage languages are useful as programming languages in their own right, that they supply a sound basis for high-level program generation technology, and that they should support features that make it possible for programmers to write staged computations without significantly changing their normal programming style. To illustrate this we provide a simple three-stage example elaborating a number of practical issues. The design of MetaML was based on two main principles that we identified as fundamental for high-level program generation, namely, cross-stage persistence and cross-stage safety. We present these principles, explain the technical problems they give rise to, and how we address with these problems in our implementation.

  • 69. Touili, Tayssir
    et al.
    Atig, Mohamed Faouzi
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computer Systems.
    Verifying parallel programs with dynamic communication structures2010In: Theoretical Computer Science, ISSN 0304-3975, E-ISSN 1879-2294, Vol. 411, p. 3460-3468Article in journal (Refereed)
  • 70.
    Uscka-Wehlou, Hanna
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Digital lines with irrational slopes2007In: Theoretical Computer Science, ISSN 0304-3975, E-ISSN 1879-2294, Vol. 377, no 1-3, p. 157-169Article in journal (Refereed)
    Abstract [en]

    How to construct a digitization of a straight line and how to be able to recognize a straight line in a set of pixels are very important topics in computer graphics. The aim of the present paper is to give a mathematically exact and consistent description of digital straight lines according to Rosenfeld's definition. The digitizations of lines with slopes 0 < a < 1, where a is irrational, are considered. We formulate a definition of digitization runs, and formulate and prove theorems containing necessary and sufficient conditions for digital straightness. The proof was successfully constructed using only methods of elementary mathematics. The developed and proved theory can be used in research into the theory of digital lines, their symmetries, translations, etc.

  • 71.
    Uscka-Wehlou, Hanna
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Two Equivalence Relations on Digital Lines with Irrational Slopes. A Continued Fraction Approach to Upper Mechanical Words2009In: Theoretical Computer Science, ISSN 0304-3975, E-ISSN 1879-2294, Vol. 410, no 38--40, p. 3655-3669Article in journal (Refereed)
    Abstract [en]

    We examine the influence of the elements of the continued fraction (CF) expansion of irrational positive a less than 1 on the construction of runs in the digitization of the positive half line y=ax or, equivalently, on the run-hierarchical structure of the upper mechanical word with slope a and intercept 0. Special attention is given to the CF elements equal to 1.We define two complementary equivalence relations on the set of slopes, based on their CF expansions. A new description of digital lines is presented; we show how to define a straight line or upper mechanical word by two sequences of positive integers fulfilling some extra conditions. These equivalence relations and this new description enable us to analyze the construction of digital lines and upper mechanical words. The analysis of suprema of equivalence classes under one of these relations leads to a result which involves Fibonacci numbers.

12 51 - 71 of 71
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