Boolean differential calculus:
The Boolean Differential Calculus (BDC) is a very powerful theory that extends the basic concepts of Boolean Algebras significantly. Its applications are based on Boolean spaces B and B n , Boolean operations, and basic structures such as Boolean Algebras and Boolean Rings, Boolean functions, Boolea...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
[San Rafael, California]
Morgan & Claypool Publishers
[2017]
|
| Schriftenreihe: | Synthesis lectures on digital circuits and systems
Lecture #52 |
| Schlagworte: | |
| Zusammenfassung: | The Boolean Differential Calculus (BDC) is a very powerful theory that extends the basic concepts of Boolean Algebras significantly. Its applications are based on Boolean spaces B and B n , Boolean operations, and basic structures such as Boolean Algebras and Boolean Rings, Boolean functions, Boolean equations, Boolean inequalities, incompletely specified Boolean functions, and Boolean lattices of Boolean functions. These basics, sometimes also called switching theory, are widely used in many modern information processing applications. The BDC extends the known concepts and allows the consideration of changes of function values. Such changes can be explored for pairs of function values as well as for whole subspaces. The BDC defines a small number of derivative and differential operations. Many existing theorems are very welcome and allow new insights due to possible transformations of problems. The available operations of the BDC have been efficiently implemented in several software packages. The common use of the basic concepts and the BDC opens a very wide field of applications. The roots of the BDC go back to the practical problem of testing digital circuits. The BDC deals with changes of signals which are very important in applications of the analysis and the synthesis of digital circuits. The comprehensive evaluation and utilization of properties of Boolean functions allow, for instance, to decompose Boolean functions very efficiently; this can be applied not only in circuit design, but also in data mining. Other examples for the use of the BDC are the detection of hazards or cryptography. The knowledge of the BDC gives the scientists and engineers an extended insight into Boolean problems leading to new applications, e.g., the use of Boolean lattices of Boolean functions |
| Beschreibung: | xii, 203 pages illustrations |
| ISBN: | 9781627059220 |
Internformat
MARC
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| 020 | |a 9781627059220 |9 978-1-6270-5922-0 | ||
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| 049 | |a DE-29T | ||
| 100 | 1 | |a Steinbach, Bernd |d 1952- |e Verfasser |0 (DE-588)1046903934 |4 aut | |
| 245 | 1 | 0 | |a Boolean differential calculus |c Bernd Steinbach, Freiberg University of Mining and Technology, Germany, Christian Posthoff, The University of West Indies, Trinidad & Tobago |
| 264 | 1 | |a [San Rafael, California] |b Morgan & Claypool Publishers |c [2017] | |
| 300 | |a xii, 203 pages |b illustrations | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Synthesis lectures on digital circuits and systems |v Lecture #52 | |
| 505 | 8 | |a 1. Basics of Boolean structures -- 1.1 Lattices and functions -- 1.2 Boolean algebras -- 1.3 Boolean rings -- 1.4 Boolean equations and inequalities -- 1.5 Lists of ternary vectors (TVL) -- | |
| 505 | 8 | |a 2. Derivative operations of Boolean functions -- 2.1 Vectorial derivative operations -- 2.2 Single derivative operations -- 2.3 m-fold derivative operations -- 2.4 Derivative operations of XBOOLE -- | |
| 505 | 8 | |a 3. Derivative operations of lattices of Boolean functions -- 3.1 Boolean lattices of Boolean functions -- 3.2 Vectorial derivative operations -- 3.3 Single derivative operations -- 3.4 m-fold derivative operations -- | |
| 505 | 8 | |a 4. Differentials and differential operations -- 4.1 Differential of a Boolean variable -- 4.2 Total differential operations -- 4.3 Partial differential operations -- 4.4 m-fold differential operations -- | |
| 505 | 8 | |a 5. Applications -- 5.1 Properties of Boolean functions -- 5.2 Solution of a Boolean equation with regard to variables -- 5.3 Computation of graphs -- 5.4 Analysis of digital circuits -- 5.5 Synthesis of digital circuits -- 5.6 Test of digital circuits -- 5.7 Synthesis by bi-decompositions -- | |
| 505 | 8 | |a 6. Solutions of the exercises -- 6.1 Solutions of chapter 1 -- 6.2 Solutions of chapter 2 -- 6.3 Solutions of chapter 3 -- 6.4 Solutions of chapter 4 -- 6.5 Solutions of chapter 5 -- Bibliography -- Authors' biographies -- Index | |
| 520 | 3 | |a The Boolean Differential Calculus (BDC) is a very powerful theory that extends the basic concepts of Boolean Algebras significantly. Its applications are based on Boolean spaces B and B n , Boolean operations, and basic structures such as Boolean Algebras and Boolean Rings, Boolean functions, Boolean equations, Boolean inequalities, incompletely specified Boolean functions, and Boolean lattices of Boolean functions. These basics, sometimes also called switching theory, are widely used in many modern information processing applications. The BDC extends the known concepts and allows the consideration of changes of function values. Such changes can be explored for pairs of function values as well as for whole subspaces. The BDC defines a small number of derivative and differential operations. Many existing theorems are very welcome and allow new insights due to possible transformations of problems. The available operations of the BDC have been efficiently implemented in several software packages. The common use of the basic concepts and the BDC opens a very wide field of applications. The roots of the BDC go back to the practical problem of testing digital circuits. The BDC deals with changes of signals which are very important in applications of the analysis and the synthesis of digital circuits. The comprehensive evaluation and utilization of properties of Boolean functions allow, for instance, to decompose Boolean functions very efficiently; this can be applied not only in circuit design, but also in data mining. Other examples for the use of the BDC are the detection of hazards or cryptography. The knowledge of the BDC gives the scientists and engineers an extended insight into Boolean problems leading to new applications, e.g., the use of Boolean lattices of Boolean functions | |
| 653 | |a Boolean Differential Calculus | ||
| 653 | |a derivative operation | ||
| 653 | |a differential operation | ||
| 653 | |a Boolean Algebra | ||
| 653 | |a Boolean Ring | ||
| 653 | |a Boolean function | ||
| 653 | |a Boolean equation | ||
| 653 | |a Boolean lattice | ||
| 653 | |a applications | ||
| 653 | |a XBOOLE | ||
| 653 | 0 | |a Differential calculus | |
| 653 | 0 | |a Algebra, Boolean | |
| 700 | 1 | |a Posthoff, Christian |d 1943- |e Verfasser |0 (DE-588)1050601068 |4 aut | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-1-6270-5617-5 |
| 830 | 0 | |a Synthesis lectures on digital circuits and systems |v Lecture #52 |w (DE-604)BV024621607 |9 52 | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-029778348 | ||
Datensatz im Suchindex
| _version_ | 1804177635125755904 |
|---|---|
| any_adam_object | |
| author | Steinbach, Bernd 1952- Posthoff, Christian 1943- |
| author_GND | (DE-588)1046903934 (DE-588)1050601068 |
| author_facet | Steinbach, Bernd 1952- Posthoff, Christian 1943- |
| author_role | aut aut |
| author_sort | Steinbach, Bernd 1952- |
| author_variant | b s bs c p cp |
| building | Verbundindex |
| bvnumber | BV044376043 |
| contents | 1. Basics of Boolean structures -- 1.1 Lattices and functions -- 1.2 Boolean algebras -- 1.3 Boolean rings -- 1.4 Boolean equations and inequalities -- 1.5 Lists of ternary vectors (TVL) -- 2. Derivative operations of Boolean functions -- 2.1 Vectorial derivative operations -- 2.2 Single derivative operations -- 2.3 m-fold derivative operations -- 2.4 Derivative operations of XBOOLE -- 3. Derivative operations of lattices of Boolean functions -- 3.1 Boolean lattices of Boolean functions -- 3.2 Vectorial derivative operations -- 3.3 Single derivative operations -- 3.4 m-fold derivative operations -- 4. Differentials and differential operations -- 4.1 Differential of a Boolean variable -- 4.2 Total differential operations -- 4.3 Partial differential operations -- 4.4 m-fold differential operations -- 5. Applications -- 5.1 Properties of Boolean functions -- 5.2 Solution of a Boolean equation with regard to variables -- 5.3 Computation of graphs -- 5.4 Analysis of digital circuits -- 5.5 Synthesis of digital circuits -- 5.6 Test of digital circuits -- 5.7 Synthesis by bi-decompositions -- 6. Solutions of the exercises -- 6.1 Solutions of chapter 1 -- 6.2 Solutions of chapter 2 -- 6.3 Solutions of chapter 3 -- 6.4 Solutions of chapter 4 -- 6.5 Solutions of chapter 5 -- Bibliography -- Authors' biographies -- Index |
| ctrlnum | (OCoLC)1001523484 (DE-599)BVBBV044376043 |
| format | Book |
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| id | DE-604.BV044376043 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T07:51:12Z |
| institution | BVB |
| isbn | 9781627059220 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029778348 |
| oclc_num | 1001523484 |
| open_access_boolean | |
| owner | DE-29T |
| owner_facet | DE-29T |
| physical | xii, 203 pages illustrations |
| publishDate | 2017 |
| publishDateSearch | 2017 |
| publishDateSort | 2017 |
| publisher | Morgan & Claypool Publishers |
| record_format | marc |
| series | Synthesis lectures on digital circuits and systems |
| series2 | Synthesis lectures on digital circuits and systems |
| spelling | Steinbach, Bernd 1952- Verfasser (DE-588)1046903934 aut Boolean differential calculus Bernd Steinbach, Freiberg University of Mining and Technology, Germany, Christian Posthoff, The University of West Indies, Trinidad & Tobago [San Rafael, California] Morgan & Claypool Publishers [2017] xii, 203 pages illustrations txt rdacontent n rdamedia nc rdacarrier Synthesis lectures on digital circuits and systems Lecture #52 1. Basics of Boolean structures -- 1.1 Lattices and functions -- 1.2 Boolean algebras -- 1.3 Boolean rings -- 1.4 Boolean equations and inequalities -- 1.5 Lists of ternary vectors (TVL) -- 2. Derivative operations of Boolean functions -- 2.1 Vectorial derivative operations -- 2.2 Single derivative operations -- 2.3 m-fold derivative operations -- 2.4 Derivative operations of XBOOLE -- 3. Derivative operations of lattices of Boolean functions -- 3.1 Boolean lattices of Boolean functions -- 3.2 Vectorial derivative operations -- 3.3 Single derivative operations -- 3.4 m-fold derivative operations -- 4. Differentials and differential operations -- 4.1 Differential of a Boolean variable -- 4.2 Total differential operations -- 4.3 Partial differential operations -- 4.4 m-fold differential operations -- 5. Applications -- 5.1 Properties of Boolean functions -- 5.2 Solution of a Boolean equation with regard to variables -- 5.3 Computation of graphs -- 5.4 Analysis of digital circuits -- 5.5 Synthesis of digital circuits -- 5.6 Test of digital circuits -- 5.7 Synthesis by bi-decompositions -- 6. Solutions of the exercises -- 6.1 Solutions of chapter 1 -- 6.2 Solutions of chapter 2 -- 6.3 Solutions of chapter 3 -- 6.4 Solutions of chapter 4 -- 6.5 Solutions of chapter 5 -- Bibliography -- Authors' biographies -- Index The Boolean Differential Calculus (BDC) is a very powerful theory that extends the basic concepts of Boolean Algebras significantly. Its applications are based on Boolean spaces B and B n , Boolean operations, and basic structures such as Boolean Algebras and Boolean Rings, Boolean functions, Boolean equations, Boolean inequalities, incompletely specified Boolean functions, and Boolean lattices of Boolean functions. These basics, sometimes also called switching theory, are widely used in many modern information processing applications. The BDC extends the known concepts and allows the consideration of changes of function values. Such changes can be explored for pairs of function values as well as for whole subspaces. The BDC defines a small number of derivative and differential operations. Many existing theorems are very welcome and allow new insights due to possible transformations of problems. The available operations of the BDC have been efficiently implemented in several software packages. The common use of the basic concepts and the BDC opens a very wide field of applications. The roots of the BDC go back to the practical problem of testing digital circuits. The BDC deals with changes of signals which are very important in applications of the analysis and the synthesis of digital circuits. The comprehensive evaluation and utilization of properties of Boolean functions allow, for instance, to decompose Boolean functions very efficiently; this can be applied not only in circuit design, but also in data mining. Other examples for the use of the BDC are the detection of hazards or cryptography. The knowledge of the BDC gives the scientists and engineers an extended insight into Boolean problems leading to new applications, e.g., the use of Boolean lattices of Boolean functions Boolean Differential Calculus derivative operation differential operation Boolean Algebra Boolean Ring Boolean function Boolean equation Boolean lattice applications XBOOLE Differential calculus Algebra, Boolean Posthoff, Christian 1943- Verfasser (DE-588)1050601068 aut Erscheint auch als Online-Ausgabe 978-1-6270-5617-5 Synthesis lectures on digital circuits and systems Lecture #52 (DE-604)BV024621607 52 |
| spellingShingle | Steinbach, Bernd 1952- Posthoff, Christian 1943- Boolean differential calculus Synthesis lectures on digital circuits and systems 1. Basics of Boolean structures -- 1.1 Lattices and functions -- 1.2 Boolean algebras -- 1.3 Boolean rings -- 1.4 Boolean equations and inequalities -- 1.5 Lists of ternary vectors (TVL) -- 2. Derivative operations of Boolean functions -- 2.1 Vectorial derivative operations -- 2.2 Single derivative operations -- 2.3 m-fold derivative operations -- 2.4 Derivative operations of XBOOLE -- 3. Derivative operations of lattices of Boolean functions -- 3.1 Boolean lattices of Boolean functions -- 3.2 Vectorial derivative operations -- 3.3 Single derivative operations -- 3.4 m-fold derivative operations -- 4. Differentials and differential operations -- 4.1 Differential of a Boolean variable -- 4.2 Total differential operations -- 4.3 Partial differential operations -- 4.4 m-fold differential operations -- 5. Applications -- 5.1 Properties of Boolean functions -- 5.2 Solution of a Boolean equation with regard to variables -- 5.3 Computation of graphs -- 5.4 Analysis of digital circuits -- 5.5 Synthesis of digital circuits -- 5.6 Test of digital circuits -- 5.7 Synthesis by bi-decompositions -- 6. Solutions of the exercises -- 6.1 Solutions of chapter 1 -- 6.2 Solutions of chapter 2 -- 6.3 Solutions of chapter 3 -- 6.4 Solutions of chapter 4 -- 6.5 Solutions of chapter 5 -- Bibliography -- Authors' biographies -- Index |
| title | Boolean differential calculus |
| title_auth | Boolean differential calculus |
| title_exact_search | Boolean differential calculus |
| title_full | Boolean differential calculus Bernd Steinbach, Freiberg University of Mining and Technology, Germany, Christian Posthoff, The University of West Indies, Trinidad & Tobago |
| title_fullStr | Boolean differential calculus Bernd Steinbach, Freiberg University of Mining and Technology, Germany, Christian Posthoff, The University of West Indies, Trinidad & Tobago |
| title_full_unstemmed | Boolean differential calculus Bernd Steinbach, Freiberg University of Mining and Technology, Germany, Christian Posthoff, The University of West Indies, Trinidad & Tobago |
| title_short | Boolean differential calculus |
| title_sort | boolean differential calculus |
| volume_link | (DE-604)BV024621607 |
| work_keys_str_mv | AT steinbachbernd booleandifferentialcalculus AT posthoffchristian booleandifferentialcalculus |