Ana Paula Tomás

University of Porto, Oporto, Porto, Portugal

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Publications (27)1.47 Total impact

  • Ana Paula Tomás, José Paulo Leal
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    ABSTRACT: We present an application of constraint logic programming to create multiple-choice questions for math quizzes. Constraints are used for the configuration of the generator, giving the user some flexibility to customize the forms of the expressions arising in the exercises. Constraints are also used to control the application of the buggy rules in the derivation of plausible wrong solutions to the quiz questions. We developed a prototype based on the core system of AGILMAT [18]. For delivering math quizzes to students, we used an automatic evaluation feature of Mooshak [8] that was improved to handle math expressions. The communication between the two systems - AgilmatQuiz and Mooshak - relies on a specially designed LaTeX based quiz format. This tool is being used at our institution to create quizzes to support assessment in a PreCalculus course for first year undergraduate students.
    International Conference on Principles and Practice of Constraint Programming, Edited by Christian Schulte, 09/2013; Springer., ISBN: 978-3-642-40626-3
  • Ana Paula Tomás
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    ABSTRACT: An orthogonal polygon of P is called "thin" if the dual graph of the partition obtained by extending all edges of P towards its interior until they hit the boundary is a tree. We show that the problem of computing a minimum guard set for either a thin orthogonal polygon or only its vertices is NP-hard, indeed APX-hard, either for guards lying on the boundary or on vertices of the polygon. For guards lying anywhere in the polygon, we show that computing an optimal guard set for the vertices of such a polygon is NP-hard.
    Proceedings of the 19th international conference on Fundamentals of Computation Theory; 08/2013
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    ABSTRACT: AGILMAT is a web application designed to help students learn Mathematics, with focus on high-school algebra and calculus drills. A modular and extensible architecture and a wizard-based configuration interface decoupled from the system core are major design features of AGILMAT. The drill expressions are specified by grammars and constraints imposed by default profiles and user options, so that AGILMAT may support distinct learning levels and stages. The core system uses symbolic manipulation and automated reasoning to provide correct answers for the drills. The paper shows how AGILMAT may be used to create and customize drills automatically.
    Advances in Web Based Learning - ICWL 2007, 6th International Conference, Edinburgh, UK, August 15-17, 2007, Revised Papers; 01/2007
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    Ana Paula Tomás, Miguel Filgueiras
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    ABSTRACT: A new algorithm for fording the minimal solutions of systems of linear Diophantine equations has recently been published. In its description the emphasis was put on the mathematical aspects of the algorithm. In complement to that, in this paper another presentation of the algorithm is given which may be of use for anyone wanting to implement it.
    04/2006: pages 73-84;
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    Ana Paula Tomás, Nelma Moreira, Nuno Pereira
    Artificial Intelligence Applications and Innovations, 3rd IFIP Conference on Artificial Intelligence Applications and Innovations (AIAI) 2006, June 7-9, 2006, Athens, Greece; 01/2006
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    ABSTRACT: We address the problem of stationing guards in vertices of a simple polygon in such a way that the whole polygon is guarded and the number of guards is minimum. It is known that this is an NP-hard Art Gallery Problem with relevant practical applications. In this paper we present an approximation method that solves the problem by successive approximations, which we intro-duced in [21]. We report on some results of its experimental evaluation and des-cribe two algorithms for characterizing visibility from a point, that we designed for its implementation.
    International Symposium on Artificial Intelligence and Mathematics (ISAIM 2006), Fort Lauderdale, Florida, USA, January 4-6, 2006; 01/2006
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    ABSTRACT: For a long time, term orderings defined by polynomial interpretations have been considered far too restrictive to be used for computer-aided termination proof of TRSs. But recently, the introduction of the dependency pairs approach achieved considerable progress w.r.t. automated termination proof, in particular by requiring from the under- lying ordering much weaker properties than the classical approach. As a consequence, the noticeable power of a combination dependency pairs/polynomial orderings yielded a regain of interest for these interpretations. We describe criteria on polynomial interpretations for them to define weakly mono- tonic orderings. From these criteria, we obtain new techniques both for mechanically checking termination using a given polynomial interpretation, and for finding such in- terpretations with full automation. With regards to automated search, we propose an original method for solving Diophantine constraints. We implemented these techniques into the CiME rewrite tool, and we provide ex- periments that show how useful polynomial orderings actually are in practice.
    Journal of Automated Reasoning 01/2005; 34:325-363. · 0.57 Impact Factor
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    ABSTRACT: To understand what people do when they do mathematics and write programs emulating that process is a continuous research topic in artificial intelligence, automated reasoning and symbolic computation. We present the first release of an web application for athematics education that is being developed within AGILMAT (Automatic Generation of Interactive Drills for Mathematics Learning, POSI/CHS/48565/2002) project. AGILMAT aims at developing a system to automatically create and solve mathematics exercises that is flexible enough to be easily customizable to different curricula and users. Its major guiding principles are: the abstraction and formal representation of the problems that may be actually solved by algebraic algorithms covered by the curricula; the customization of these models by adding further constraints; and designing flexible solvers that emulate the steps students usually take to solve the generated drills.
    Twelfth Portuguese Conference on Artificial Intelligence (EPIA-2005); 01/2005
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    Ana Paula Tomás, António Leslie Bajuelos
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    ABSTRACT: We propose Inflate-Paste { a new technique for generating orthogonal polygons with a given number of vertices from a unit square based on gluing rectangles. It is dual to Inflate-Cut { a technique we introduced in (12) that works by cutting rectangles.
    Computational Science and Its Applications - ICCSA 2004, International Conference, Assisi, Italy, May 14-17, 2004, Proceedings, Part III; 01/2004
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    ABSTRACT: Given an orthogonal polygon P , let j (P )j be the number of rectangles that result when we partition P by extending the edges incident to reex vertices towards INT(P ). In (4) we have shown that j (P )j 1 + r + r 2 , where r is the number of reex vertices of P. We shall now give sharper bounds both for maxP j (P )j and minP j (P )j. Moreover, we characterize the structure of orthogonal polygons in general position for which these new bounds are exact. We also present bounds on the area of grid n-ogons and characterize those having the largest and the smallest area.
    Computational Science and Its Applications - ICCSA 2004, International Conference, Assisi, Italy, May 14-17, 2004, Proceedings, Part III; 01/2004
  • Lecture Notes in Computer Science 01/2004; 3045:127-136. · 0.51 Impact Factor
  • 01/2004;
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    ABSTRACT: We propose an anytime algorithm to compute successively better approximations of the optimum of Minimum Vertex Guard. Though the presentation is focused on polygons, the work may be directly extended to terrains along the lines of (4). A major idea in our approach is to explore dominance of visibility regions to rst detect pieces that are more dicult to guard.
    Computational Science - ICCS 2003, International Conference, Melbourne, Australia and St. Petersburg, Russia, June 2-4, 2003. Proceedings, Part I; 01/2003
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    Ana Paula Tomás, António Leslie Bajuelos
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    ABSTRACT: We propose two dieren t methods for generating random or- thogonal polygons with a given number of vertices. One is a polynomial time algorithm and it is supported by a technique we developed to ob- tain polygons with an increasing number of vertices starting from a unit square. The other follows a constraint programming approach and gives great control on the generated polygons. In particular, it may be used to nd all n-vertex orthogonal polygons with no collinear edges that can be drawn in an n 2 n 2 grid, for small n, with symmetries broken.
    Current Topics in Artificial Intelligence, 10th Conference of the Spanish Association for Artificial Intelligence, CAEPIA 2003, and 5th Conference on Technology Transfer, TTIA 2003, San Sebastian, Spain, November 12-14, 2003. Revised Selected Papers; 01/2003
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    Ana Paula Tomás, José Paulo Leal
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    ABSTRACT: We propose an interesting application of Constraint Logic Programming to automatic generation and explanation of mathematics exercises. A particular topic in mathematics is considered to investigate and illustrate the advantages of using the CLP paradigm. The goal is to develop software components that make the formulation and explanation of exercises easier. We describe exercises by grammars which enables us to get specialized forms almost for free, by imposing further conditions through constraints. To de.ne the grammars we concentrate on the solving procedures that are taught instead of trying to abstract an exercise template from a sample of similar exercises. Prototype programs indicate that Constraint Logic Programming frameworks may be adequate to implement such a tool. These languages have the right expressiveness to encode control on the system in an elegant and declarative way.
    Practical Aspects of Declarative Languages, 5th International Symposium, PADL 2003, New Orleans, LA, USA, January 13-14, 2003, Proceedings; 01/2003
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    Ana Paula Tomás
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    ABSTRACT: We present an application of Constraint Logic Programming (CLP) for finding the minimum number and location of count-posts at urban roundabouts so as to obtain origin-destination data at minimum cost. By finding nice mathematical properties, we were able to model this problem as a constraint satisfaction problem in finite domains, and use CLP(FD) systems to solve it, with almost no implementation effort and very quickly.
    MICAI 2002: Advances in Artificial Intelligence, Second Mexican International Conference on Artificial Intelligence, Merida, Yucatan, Mexico, April 22-26, 2002, Proceedings; 01/2002
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    Ana Paula Tomás, Miguel Filgueiras
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    ABSTRACT: In the development of algorithms for nding the minimal solutions of systems of linear Diophantine equations, little use has been made (to our knowledge) of the results by Stanley using the geometric properties of the solution space. Building upon these results, we present a new algorithm, and we suggest the use of geometric properties of the solution space in nding bounds for searching solutions and in having a qualitative evaluation of the diculty in solving a given system. word problems, or combinatorics. In terms of the development of algorithms for solving this problem, little use has been made (to our knowledge) of the results by Stanley using the geometric properties of the solution space (14, 15), in particular, his characterization of the generating function of the solutions monoid. Building upon these results, we present a new algorithm, which is a refor- mulation of the Slopes Algorithm we described previously for solving a single equation (6), and we suggest the use of geometric properties of the solution space in nding bounds for searching solutions and in having a qualitative evaluation of the diculty in solving a given system. We also note that, as a direct conse- quence of Stanley's results, the algorithm by Domenjoud (3) can be improved.
    Rewriting Techniques and Applications, 8th International Conference, RTA-97, Sitges, Spain, June 2-5, 1997, Proceedings; 01/1997
  • Eric Domenjoud, Ana Paula Tomás
    Principles and Practice of Constraint Programming - CP'95, First International Conference, CP'95, Cassis, France, September 19-22, 1995, Proceedings; 01/1995
  • Miguel Filgueiras, Ana Paula Tomás
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    ABSTRACT: A method is given to solve ∑ i=1 N a i x i =∑ j=1 M b j y j , a i ,b j ,x i ,y j ∈ℕ. At first the equation ax=by+cz+v; a,b,c,x,y∈ℕ, v∈ℤ is considered and the solution with (x,y,z) minimal in componentwise ordering are determined by using the congruence by+cz≡-v(moda). Then the general problem is reduced to this case. The algorithm is extensively compared with other methods.
    Journal of Symbolic Computation 01/1995; 19:507-526. · 0.39 Impact Factor
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    Miguel Filgueiras, Ana Paula Tomás
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    ABSTRACT: We present some recent results from our research on methods for nding the minimal solutions to linear Diophantine equations over the naturals. We give an overview of a family of methods we developed and describe two of them, called Slopes algorithm and Rectangles algorithm. From empirical evidence obtained by directly comparing our methods with others, and which is partly presented here, we are convinced that ours are the fastest known to date when the equation coecien ts are not too small (ie., greater than 2 or 3).
    Progress in Artificial Intelligence, 6th Portuguese Conference on Artificial Intelligence, EPIA '93, Porto, Portugal, October 6-8, 1993, Proceedings; 01/1993