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Boolean function complexity /
By considering the size of the logical network needed to perform a given computational task, the intrinsic difficulty of that task can be examined. Boolean function complexity, the combinatorial study of such networks, is a subject that started back in the 1950s and has today become one of the most...
| Clasificación: | Libro Electrónico |
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| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge ; New York, NY, USA :
Cambridge University Press,
1992.
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| Colección: | London Mathematical Society lecture note series ;
169. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; Title; Copyright; Contents; Preface; List of Participants; Relationships Between Monotone and Non-Monotone Network Complexity; Abstract; 1. Introduction; 2. Monotone boolean networks; 3. A framework for relating combinational and monotone network complexity; 4. Slice functions and their properties; 5. Conclusion; 6. Further reading; 7. Appendix
- another application of theorem 3.5; References; On Read-Once Boolean Functions; Abstract; 1. Introduction; 2. Definitions and notations; 3. Characterization of read-once functions and generalizations; 3.1. Characterization
- 3.2. Generalization to read-once on a subset of the variables3.3. Functions with the t-intersection property.; 4. Read-once functions and the randomized boolean decision tree model; Acknowledgments; References; Boolean Function Complexity: a Lattice-Theoretic Perspective; Abstract; 1. Introduction; 2. Boolean computation: a lattice-theoretic view; 2.1. Computational equivalence and replaceability; 2.2. The case of distributive lattices; 2.3. Applications; 3. An alternative model for free distributive lattices; 3.1. Characteristics of the combinatorial model
- 4. Towards Separating mBWBP from mNCL4.1. A lower bound on size; 4.2. There is no monotone barrington gadget; 5. Conclusion; References; On Submodular Complexity Measures; 1. Introduction; 2. Definitions and example of submodular complexity measures; 3. Main result; References; Why is Boolean Complexity Theory so Difficult?; 1. Introduction; 2. Algebraic structures; 3. Cancellations in the samuelson-berkowitz algorithm; 4. Simultaneous lower bounds on size and depth; References; The Multiplicative Complexity of Boolean Quadratic Forms, a Survey.; 1. Introduction
- 2. The multiplicative complexity of single boolean quadratic forms3. Independence and lower bounds for two boolean quadratic forms; 4. The multiplicative complexity of pairs of quadratic boolean forms; References; Some Problems Involving Razborov-Smolensky Polynomials; 1. Introduction; 1.1. Polynomials and circuit complexity; 1.2. The programs-over-monoid model; 1.3. Polynomials and programs over groups; 2. The small image-set conjecture; 3. The intersection conjecture; 4. Making change in an abelian group; 5. Consequences; 6. Acknowledgements; References