Phase transition in the countdown problem

Lacasa Saiz de Arce, Lucas and Luque Serrano, Bartolome (2012). Phase transition in the countdown problem. "Physical Review e", v. 86 ; pp.. ISSN 1539-3755. https://doi.org/10.1103/PhysRevE.86.010105.

Description

Title: Phase transition in the countdown problem
Author/s:
  • Lacasa Saiz de Arce, Lucas
  • Luque Serrano, Bartolome
Item Type: Article
Título de Revista/Publicación: Physical Review e
Date: 2012
ISSN: 1539-3755
Volume: 86
Subjects:
Faculty: E.T.S.I. Aeronáuticos (UPM)
Department: Matemática Aplicada y Estadística [hasta 2014]
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

We present a combinatorial decision problem, inspired by the celebrated quiz show called Countdown, that involves the computation of a given target number T from a set of k randomly chosen integers along with a set of arithmetic operations. We find that the probability of winning the game evidences a threshold phenomenon that can be understood in the terms of an algorithmic phase transition as a function of the set size k. Numerical simulations show that such probability sharply transitions from zero to one at some critical value of the control parameter, hence separating the algorithm's parameter space in different phases. We also find that the system is maximally efficient close to the critical point. We derive analytical expressions that match the numerical results for finite size and permit us to extrapolate the behavior in the thermodynamic limit.

Funding Projects

TypeCodeAcronymLeaderTitle
Madrid Regional GovernmentMODELICO FIS2009-13690UnspecifiedUnspecifiedUnspecified

More information

Item ID: 16710
DC Identifier: http://oa.upm.es/16710/
OAI Identifier: oai:oa.upm.es:16710
DOI: 10.1103/PhysRevE.86.010105
Official URL: http://journals.aps.org/pre/abstract/10.1103/PhysRevE.86.010105
Deposited by: Memoria Investigacion
Deposited on: 13 Nov 2014 17:26
Last Modified: 13 Nov 2014 17:26
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