A system simulating representation change phenomena while problem solving

Hernando, A.; Ledesma, Luis de; Laita, Luis M.

doi:10.1016/j.matcom.2007.06.009

Cited by 3 publications

(2 citation statements)

References 14 publications

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“…Indeed, applying different representation changes to a problem may result in the possibility of having different reduced linear problem spaces. Some research has been already made so as to getting automatic representation changes [22], either before the resolution process is started [11] or even while this process is being performed [13]. A possibility of extending this research line may involve developing different representation changes suitable to obtain good linear reduction to problems.…”

Section: Applying the Techniques To Non-linear Problem Spacesmentioning

confidence: 99%

New methods for proving the impossibility to solve problems through reduction of problem spaces

Hernando

2009

Ann Math Artif Intell

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Problem solvers are computational systems which make use of different search algorithms for solving problems. Sometimes, while employing such search algorithms, problem solvers may prove to be inefficient and take too great an effort so as to showing that the problem has no solution. For such cases, in this paper we explain a technique which provides a quick proof that finding a solution is actually impossible. This technique results in reducing the number and simplifying the topology of the states which shape a problem space. Hence, we show and prove efficient new techniques intended to find such reductions which may result to be very useful for many problems.

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Section: Applying the Techniques To Non-linear Problem Spacesmentioning

confidence: 99%

New methods for proving the impossibility to solve problems through reduction of problem spaces

Hernando

2009

Ann Math Artif Intell

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“…A representation change consisting in dropping those irrelevant elements from the representation not only results in a new conception of the problem, but it may also involve an outstanding improvement in the efficiency of the problem's resolution. In [7] we have already studied mathematically the relationship between a given problem and the need for performing suitable representation changes. Using this technique for measuring and modifying relevance, we have so far implemented a prototype problem solver able to perform representation changes while problem solving.…”

Section: Introductionmentioning

confidence: 99%

A technique for dynamically measuring and modifying relevance while problem solving

Hernando

Ledesma

2009

Rev. R. Acad. Cien. Serie A. Mat.

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Although there is general agreement that efficiency of problem resolution is strongly related to the problem representation adopted, computer problem solvers have been traditionally designed to keep the same representation throughout the whole of the problem solving process. A system able to change representation whilst the actual problem solving process occurs has advantages over traditional ones, not only because a representation change can improve the efficiency of problem resolution (as already proven through much research), but also because the choice of the most suitable representation may be decisively enhanced after learning about the problem during its resolution process. A natural and interesting way of performing representation changes is related to detecting irrelevant elements which can be removed out of the problem representation. In this paper, we deal formally with a new technique for assigning and changing the relevance of the elements involved in the representation during the problem resolution, on behalf of their respective importance so as to actually solve the problem. Una técnica para medir y modificar dinámicamente la relevancia en la resolución de problemasResumen. Aunque existe un consenso general sobre la fuerte dependencia entre la eficiencia en la resolución de problemas y la representación de los mismos que se adopta, los programas resolvedores de problemas tradicionalmente se han diseñado teniendo en cuentaúnicamente una sola representación a lo largo de todo el proceso de resolución. Un sistema capaz de cambiar la representación mientras el mismo proceso de resolución tiene lugar ofrece ventajas respecto de los tradicionales, no sólo porque ciertos cambios de representación pueden mejorar la eficiencia del proceso de resolución (como muchas investigaciones han demostrado), sino también debido a que la tarea de seleccionar la representación más adecuada para un problema puede facilitarse decisivamente mediante el conocimiento adquirido durante el proceso de su resolución. Una manera interesante y natural de ejecutar cambios de representación se apoya en detectar la información irrelevante que puede eliminarse de la representación del problema. En el presente trabajo, presentamos formalmente una nueva técnica para asignar y modificar valores de relevancia a los elementos que integran la representación de los problemas durante el mismo proceso de resolución, de acuerdo con la importancia que tienen para resolverlos.p n+1 = max{R + floor(k 1 · R/R) − k 1 , th} = max{R + k 1 − k 1 , th} = max{R, th}.Since R > th, we have that p n+1 = R iii) We have that:Since k 1 ≤ th ≤ p n and floor(−k 1 /p n ) = −1, we have that p n+1 ≤ max{p n − 1, th}.Since th < R and R < p n , we have that th ≤ p n − 1 and therefore p n+1 ≤ max{p n − 1, th} = p n − 1 < p n .Besides, we have that p n+1 ≥ R p n+1 = max{f (p n , R), th} ≥ max{f (R, R), th} = R.Theorem 2 If N = 0, then we have that:∃n ∈ N ∀m ≥ n p m = R PROOF. We will prove that ∃n ≥ 0 such that p n = R. Once we have proved it, we will prove this lemma ...

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Showing the non-existence of solutions in systems of linear Diophantine equations

Hernando

Ledesma

Laita

2009

Mathematics and Computers in Simulation

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A system simulating representation change phenomena while problem solving

Cited by 3 publications

References 14 publications

New methods for proving the impossibility to solve problems through reduction of problem spaces

New methods for proving the impossibility to solve problems through reduction of problem spaces

A technique for dynamically measuring and modifying relevance while problem solving

Showing the non-existence of solutions in systems of linear Diophantine equations

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