Analysis of Minimal Boolean Circuits

Circuit complexity, a branch of computational complexity theory, has seen limited progress in establishing lower bounds for the minimum size of circuits that solve NP-complete problems. Existing bounds primarily apply to restricted families of circuits, such as constant-depth or monotone circuits. I...

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Detalles Bibliográficos
Autor: Celaya Rodríguez, Joseba
Tipo de recurso: tesis de maestría
Fecha de publicación:2025
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/125022
Acceso en línea:https://hdl.handle.net/20.500.14352/125022
Access Level:acceso abierto
Palabra clave:004(043.3)
Circuit complexity
Boolean functions
Minimal circuits
Graph analysis
Endogamy
Complejidad de circuitos
Funciones booleanas
Circuitos míınimos
Análisis de grafos
Endogamia
Informática (Informática)
33 Ciencias Tecnológicas
Descripción
Sumario:Circuit complexity, a branch of computational complexity theory, has seen limited progress in establishing lower bounds for the minimum size of circuits that solve NP-complete problems. Existing bounds primarily apply to restricted families of circuits, such as constant-depth or monotone circuits. Identifying an NP problem that requires superpolynomial-size circuits would imply that P ̸= NP, highlighting the difficulty of this challenge. In this work, we propose metrics for analyzing Boolean functions and the circuits that implement them. We apply these metrics to complete sets of minimum-size circuits, with the aim of studying their structure and understanding what makes a function require large circuits.