2026-06-28T15:28:33Zhttps://docta.ucm.es/rest/oai/requestoai:docta.ucm.es:20.500.14352/1056372025-03-18T15:17:26Zcom_20.500.14352_1col_20.500.14352_8
Docta Complutense
advisor
Rodríguez Laguna, Ismael
advisor
Rubio Díez, Fernando
author
Gómez Abejón, Martín
2024-07-04T14:29:35Z
2024-07-04T14:29:35Z
2023
https://hdl.handle.net/20.500.14352/105637
In this work, we discuss and prove several theoretical results related to computability and complexity properties of an opinion dynamics model we define. We also try to find low-complexity heuristics and algorithms which let us obtain approximate solutions of an NP-complete problem based on our model, and run simulations to determine to what extent these heuristics are effective. Although we conclude that most practical problems
related to our model are undecidable in the infinite case and PSPACE-complete or NP-complete in the finite case, the obtained low-complexity algorithms are effective at solving instances whose structure and properties are similar to those of real-world examples.En este trabajo, se abordan y demuestran varios resultados teóricos relacionados con las propiedades de computabilidad y complejidad de un modelo de dinámica de opiniones que definimos. También intentamos encontrar heurísticas y algoritmos de baja complejidad que nos permitan obtener soluciones aproximadas de un problema NP-completo basado en nuestro modelo, y ejecutamos simulaciones para determinar en qué medida estas heurísticas son efectivas. A pesar de que concluimos que la mayoría de problemas prácticos relacionados con nuestro modelo son indecidibles en el caso infinito y PSPACE-completos o NP-completos en el caso finito, los algoritmos de baja complejidad obtenidos son efectivos resolviendo instancias cuya estructura y propiedades son parecidas a las de ejemplos del mundo real.
eng
Attribution 4.0 International
Computability and Complexity of opinion dynamics
bachelor thesis
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
URL
https://docta.ucm.es/bitstreams/1b57c91f-d69d-4f53-88a4-e06644f7168b/download
File
MD5
1f5b4b71b93cc00f355e853ae58d2ef9
1111169
application/pdf
52736_MARTIN_GOMEZ_ABEJON_VersionFinal.pdf_2404368_1948321188.pdf
URL
https://docta.ucm.es/bitstreams/b679f7c4-cae5-4d55-840c-68a1b1f53e05/download
File
MD5
0f7be25dbc02c12d5de974e14da6f2f9
150033
text/plain
52736_MARTIN_GOMEZ_ABEJON_VersionFinal.pdf_2404368_1948321188.pdf.txt