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...
Gespeichert in:
| Weitere Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge ; New York, NY, USA :
Cambridge University Press,
1992.
|
| Schriftenreihe: | London Mathematical Society lecture note series ;
169. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | 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 challenging and vigorous areas of theoretical computer science. The papers in this book stem from the London Mathematical Society Symposium on Boolean Function Complexity held at Durham University in July 1990. The range of topics covered will be of interest to the newcomer to the field as well as the expert, and overall the papers are representative of the research presented at the Symposium. Anyone with an interest in Boolean Function complexity will find that this book is a necessary purchase. |
| Beschreibung: | Papers from the Symposium on Boolean Function Complexity, held July, 1990, at Durham University and sponsored by the London Mathematical Society. |
| Beschreibung: | 1 online resource (201 pages) : illustrations |
| Bibliographie: | Includes bibliographical references (pages 198-201). |
| ISBN: | 9781107361720 1107361729 9780511526633 0511526636 |
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| 504 | |a Includes bibliographical references (pages 198-201). | ||
| 588 | 0 | |a Print version record. | |
| 520 | |a 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 challenging and vigorous areas of theoretical computer science. The papers in this book stem from the London Mathematical Society Symposium on Boolean Function Complexity held at Durham University in July 1990. The range of topics covered will be of interest to the newcomer to the field as well as the expert, and overall the papers are representative of the research presented at the Symposium. Anyone with an interest in Boolean Function complexity will find that this book is a necessary purchase. | ||
| 505 | 0 | |a 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 | |
| 505 | 8 | |a 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 | |
| 505 | 8 | |a 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 | |
| 505 | 8 | |a 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 | |
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| contents | 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 |
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| dewey-raw | 511.3/24 |
| dewey-search | 511.3/24 |
| dewey-sort | 3511.3 224 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | ZDB-4-EBA-ocn839304312 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:25:17Z |
| institution | BVB |
| isbn | 9781107361720 1107361729 9780511526633 0511526636 |
| language | English |
| oclc_num | 839304312 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (201 pages) : illustrations |
| psigel | ZDB-4-EBA |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | Cambridge University Press, |
| record_format | marc |
| series | London Mathematical Society lecture note series ; |
| series2 | London Mathematical Society lecture note series ; |
| spelling | Boolean function complexity / edited by M.S. Paterson. Cambridge ; New York, NY, USA : Cambridge University Press, 1992. 1 online resource (201 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier London Mathematical Society lecture note series ; 169 Papers from the Symposium on Boolean Function Complexity, held July, 1990, at Durham University and sponsored by the London Mathematical Society. Includes bibliographical references (pages 198-201). Print version record. 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 challenging and vigorous areas of theoretical computer science. The papers in this book stem from the London Mathematical Society Symposium on Boolean Function Complexity held at Durham University in July 1990. The range of topics covered will be of interest to the newcomer to the field as well as the expert, and overall the papers are representative of the research presented at the Symposium. Anyone with an interest in Boolean Function complexity will find that this book is a necessary purchase. 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 Computational complexity Congresses. Algebra, Boolean. http://id.loc.gov/authorities/subjects/sh85003429 Complexité de calcul (Informatique) Congrès. Algèbre de Boole. MATHEMATICS Algebra General. bisacsh Algebra, Boolean fast Computational complexity fast Komplexitätstheorie gnd http://d-nb.info/gnd/4120591-1 Boolesche Funktion gnd http://d-nb.info/gnd/4146281-6 Boolean-functions. gtt Boole, algèbre de Congrès. ram Complexité de calcul (Informatique) Congrès. ram Conference papers and proceedings fast Paterson, Michael S. has work: Boolean function complexity (Text) https://id.oclc.org/worldcat/entity/E39PCXBtMyBW7wpcRwQHCKCytX https://id.oclc.org/worldcat/ontology/hasWork Print version: Boolean function complexity. Cambridge ; New York, NY, USA : Cambridge University Press, 1992 0521408261 (DLC) 93111192 (OCoLC)28063747 London Mathematical Society lecture note series ; 169. http://id.loc.gov/authorities/names/n42015587 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=552529 Volltext |
| spellingShingle | Boolean function complexity / London Mathematical Society lecture note series ; 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 Computational complexity Congresses. Algebra, Boolean. http://id.loc.gov/authorities/subjects/sh85003429 Complexité de calcul (Informatique) Congrès. Algèbre de Boole. MATHEMATICS Algebra General. bisacsh Algebra, Boolean fast Computational complexity fast Komplexitätstheorie gnd http://d-nb.info/gnd/4120591-1 Boolesche Funktion gnd http://d-nb.info/gnd/4146281-6 Boolean-functions. gtt Boole, algèbre de Congrès. ram Complexité de calcul (Informatique) Congrès. ram |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85003429 http://d-nb.info/gnd/4120591-1 http://d-nb.info/gnd/4146281-6 |
| title | Boolean function complexity / |
| title_auth | Boolean function complexity / |
| title_exact_search | Boolean function complexity / |
| title_full | Boolean function complexity / edited by M.S. Paterson. |
| title_fullStr | Boolean function complexity / edited by M.S. Paterson. |
| title_full_unstemmed | Boolean function complexity / edited by M.S. Paterson. |
| title_short | Boolean function complexity / |
| title_sort | boolean function complexity |
| topic | Computational complexity Congresses. Algebra, Boolean. http://id.loc.gov/authorities/subjects/sh85003429 Complexité de calcul (Informatique) Congrès. Algèbre de Boole. MATHEMATICS Algebra General. bisacsh Algebra, Boolean fast Computational complexity fast Komplexitätstheorie gnd http://d-nb.info/gnd/4120591-1 Boolesche Funktion gnd http://d-nb.info/gnd/4146281-6 Boolean-functions. gtt Boole, algèbre de Congrès. ram Complexité de calcul (Informatique) Congrès. ram |
| topic_facet | Computational complexity Congresses. Algebra, Boolean. Complexité de calcul (Informatique) Congrès. Algèbre de Boole. MATHEMATICS Algebra General. Algebra, Boolean Computational complexity Komplexitätstheorie Boolesche Funktion Boolean-functions. Boole, algèbre de Congrès. Conference papers and proceedings |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=552529 |
| work_keys_str_mv | AT patersonmichaels booleanfunctioncomplexity |