Network AlgebraNetwork Algebra considers the algebraic study of networks and their behaviour. It contains general results on the algebraic theory of networks, recent results on the algebraic theory of models for parallel programs, as well as results on the algebraic theory of classical control structures. The results are presented in a unified framework of the calculus of flownomials, leading to a sound understanding of the algebraic fundamentals of the network theory. The term 'network' is used in a broad sense within this book, as consisting of a collection of interconnecting cells, and two radically different specific interpretations of this notion of networks are studied. One interpretation is additive, when only one cell is active at a given time - this covers the classical models of control specified by finite automata or flowchart schemes. The second interpretation is multiplicative, where each cell is always active, covering models for parallel computation such as Petri nets or dataflow networks. More advanced settings, mixing the two interpretations are included as well. Network Algebra will be of interest to anyone interested in network theory or its applications and provides them with the results needed to put their work on a firm basis. Graduate students will also find the material within this book useful for their studies. |
Contents
| 3 | |
Network Algebra and its applications | 17 |
Networks modulo graph isomorphism 57 | 55 |
Algebraic models for branching constants | 91 |
Network behaviour 123 | 122 |
Elgot theories | 147 |
Kleene theories | 169 |
Flowchart schemes 197 | 196 |
Automata | 223 |
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Common terms and phrases
acyclic AddRel(D algebraic structure algebraic theory arbitrary arrows atomic automata automaton axiomatic systems basic behaviour bijections bisimulation BNA axioms branching constants calculus cells chapter coalgebraic congruence relation connections corresponding data-flow networks defined definition denotes described deterministic dual duality Elgot theory enzymatic rule equations equivalence relation equivalent example EXERCISES AND PROBLEMS finite flowchart flownomial expressions Floyd-Hoare logic functions hence i(la idempotent identity input input-output interface interpretation isomorphic iteration job stream Kleene theory languages Lemma LR-flow matrix theory minimal mixalgebra monoid morphism multiplicative network algebra nf-pairs nondeterministic notation obtained output parallel Petri nets presented PROBLEMS SEC process algebra proof prove regular expressions relations resp restriction result satisfies semantics simulation surjective symocat synchronous Theorem transformation transition tuple unique valid variables xy-Rels xy-symocats αβ αγ αδ