'Et moi ... ~ si j'avait su comment en revenir. One service mathematics has rendered thl je n'y serais point aile: human race. It has put common sense back where it belongs. on the topmost shelf nexl Jules Verne to the dusty canister labelled 'discarded non· The series is divergent; therefore we may be sense'. Eric T. Bell able to do something with it O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non· Iinearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and fO! other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com· puter science ... .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.
Reihe
Auflage
Sprache
Verlagsort
Zielgruppe
Für höhere Schule und Studium
Für Beruf und Forschung
Research
Produkt-Hinweis
Fadenheftung
Gewebe-Einband
Illustrationen
Maße
Höhe: 240 mm
Breite: 164 mm
Dicke: 32 mm
Gewicht
ISBN-13
978-0-7923-0525-5 (9780792305255)
DOI
10.1007/978-94-009-0487-3
Schweitzer Klassifikation
1 Introduction.- 2 Asynchronous processes and their interpretation.- 2.1 Asynchronous processes.- 2.2 Petri nets.- 2.3 Signal graphs.- 2.4 The Muller model.- 2.5 Parallel asynchronous flow charts.- 2.6 Asynchronous state machines.- 2.7 Reference notations.- 3 Self-synchronizing codes.- 3.1 Preliminary definitions.- 3.2 Direct-transition codes.- 3.3 Two-phase codes.- 3.4 Double-rail code.- 3.5 Code with identifier.- 3.6 Optimally balanced code.- 3.7 On the code redundancy.- 3.8 Differential encoding.- 3.9 Reference notations.- 4 Aperiodic circuits.- 4.1 Two-phase implementation of finite state machine.- 4.2 Completion indicators and checkers.- 4.3 Synthesis of combinatorial circuits.- 4.4 Aperiodic flip-flops.- 4.5 Canonical aperiodic implementations of finite state machines.- 4.6 Implementation with multiple phase signals.- 4.7 Implementation with direct transitions.- 4.8 On the definition of an aperiodic state machine.- 4.9 Reference notations.- 5 Circuit modelling of control flow.- 5.1 The modelling of Petri nets.- 5.2 The modelling of parallel asynchronous flow charts.- 5.3 Functional completeness and synthesis of semi-modular circuits.- 5.4 Synthesis of semi-modular circuits in limited bases.- 5.5 Modelling pipeline processes.- 5.6 Reference notations.- 6 Composition of asynchronous processes and circuits.- 6.1 Composition of asynchronous processes.- 6.2 Composition of aperiodic circuits.- 6.3 Algebra of asynchronous circuits.- 6.4 Reference notations.- 7 The matching of asynchronous processes and interface organization.- 7.1 Matched asynchronous processes.- 7.2 Protocol.- 7.3 The matching asynchronous process.- 7.4 The T2 interface.- 7.5 Asynchronous interface organization.- 7.6 Reference notations.- 8 Analysis of asynchronous circuits and processes.- 8.1 The reachability analysis.- 8.2 The classification analysis.- 8.3 The set of operational states.- 8.4 The effect of non-zero wire delays.- 8.5 Circuit Petri nets.- 8.6 On the complexity of analysis algorithms.- 8.7 Reference notations.- 9 Anomalous behaviour of logical circuits and the arbitration problem.- 9.1 Arbiters.- 9.2 Oscillatory anomaly.- 9.3 Meta-stability anomaly.- 9.4 Designing correctly-operating arbiters.- 9.5 "Bounded" arbiters and safe inertial delays.- 9.6 Reference notations.- 10 Fault diagnosis and self-repair in aperiodic circuits.- 10.1 Totally self-checking combinational circuits.- 10.2 Totally self-checking sequential machines.- 10.3 Fault detection in autonomous circuits.- 10.4 Self-repair organization for aperiodic circuits.- 10.5 Reference notations.- 11 Typical examples of aperiodic design modules.- 11.1 The JK-flip-flop.- 11.2 Registers.- 11.3 Pipeline registers.- 11.4 Converting single-rail signals into double-rail ones.- 11.5 Counters.- 11.6 Reference notations.- Editor's Epilogue.- References.
