### Abstract

We discuss the collective behaviour of a set of operators and variables that constitute a program and the emergence of meaningful computational properties in the language of statistical mechanics. This is done by appropriately modifying available Monte Carlo methods to deal with hierarchical structures. The study suggests, in analogy with simulated annealing, a method to automatically design programs. Reasonable solutions can be found, at low temperatures, when the method is applied to simple toy problems such as finding an algorithm that determines the roots of a function or one that makes a nonlinear regression. Peaks in the specific heat are interpreted as signalling phase transitions which separate regions where different algorithmic strategies are used to solve the problem.

Original language | English |
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Article number | 006 |

Pages (from-to) | 10355-10361 |

Number of pages | 7 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 39 |

Issue number | 33 |

DOIs | |

Publication status | Published - 18 Aug 2006 |

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### Cite this

*Journal of Physics A: Mathematical and General*,

*39*(33), 10355-10361. [006]. https://doi.org/10.1088/0305-4470/39/33/006

}

*Journal of Physics A: Mathematical and General*, vol. 39, no. 33, 006, pp. 10355-10361. https://doi.org/10.1088/0305-4470/39/33/006

**Statistical mechanics of program systems.** / Neirotti, Juan P.; Caticha, Nestor.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Statistical mechanics of program systems

AU - Neirotti, Juan P.

AU - Caticha, Nestor

PY - 2006/8/18

Y1 - 2006/8/18

N2 - We discuss the collective behaviour of a set of operators and variables that constitute a program and the emergence of meaningful computational properties in the language of statistical mechanics. This is done by appropriately modifying available Monte Carlo methods to deal with hierarchical structures. The study suggests, in analogy with simulated annealing, a method to automatically design programs. Reasonable solutions can be found, at low temperatures, when the method is applied to simple toy problems such as finding an algorithm that determines the roots of a function or one that makes a nonlinear regression. Peaks in the specific heat are interpreted as signalling phase transitions which separate regions where different algorithmic strategies are used to solve the problem.

AB - We discuss the collective behaviour of a set of operators and variables that constitute a program and the emergence of meaningful computational properties in the language of statistical mechanics. This is done by appropriately modifying available Monte Carlo methods to deal with hierarchical structures. The study suggests, in analogy with simulated annealing, a method to automatically design programs. Reasonable solutions can be found, at low temperatures, when the method is applied to simple toy problems such as finding an algorithm that determines the roots of a function or one that makes a nonlinear regression. Peaks in the specific heat are interpreted as signalling phase transitions which separate regions where different algorithmic strategies are used to solve the problem.

UR - http://www.scopus.com/inward/record.url?scp=33746926758&partnerID=8YFLogxK

UR - https://iopscience.iop.org/article/10.1088/0305-4470/39/33/006/meta

U2 - 10.1088/0305-4470/39/33/006

DO - 10.1088/0305-4470/39/33/006

M3 - Article

AN - SCOPUS:33746926758

VL - 39

SP - 10355

EP - 10361

JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

SN - 0305-4470

IS - 33

M1 - 006

ER -