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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| 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 |
| 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. |
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