Universal Theory of Automata A Categorical Approach [Paperback]

1. Unified Representation of Automata.- deterministic, nondeterministic, stochastic, linear, bilinear, and topological automata (1.11.7); monoidal categories (1.81.10); automata in monoidal categories (1.111.14).- 2. Some Problems in Automata Theory.- behavior, reduction, minimization and realization of deterministic automata (2.12.6); nondeterministic automata (2.7); transition monoids (2.8); structure theory (2.9).- 3. General Concepts of Reduction, Minimization and Realization.- concept of systematics (3.1); reduced, minimal and realizing systems and subsystematics (3.23.3); reduction theorem (3.4); minimal realization theorem (3.6).- 4. Behavior of Automata in Closed Categories: The Deterministic Case.- extended output morphisms and coproducts (4.2); machine morphisms and closed categories (4.34.4); characterization of automata (4.5); behavior and image-factorization (4.64.7); behavior characterization (4.8); list of examples (4.9).- 5. Reduction and Minimization of Automata in Closed Categories.- systematic of automata in closed categories (5.2); minimal realization theorem (5.3); observable and reduced automata (5.4); reduction and minimization theorem (5.5); monoid automata and transition monoids (5.65.7).- 6. Behavior of Automata in Pseudoclosed Categories: The Nondeterministic Case.- automata in pseudoclosed categories  extended output, machine morphism and behavior (6.26.4); characterization of machine morphisms and behaviors (6.66.7); list of examples (6.8).- 7. Reduction and Minimization of Automata in Pseudoclosed Categories.- construction of reduced and observable automata (7.27.4); realization (7.5); systematic of automata in pseudoclosed categories (7.6); reduction theorem (7.7); minimization theorem (7.8); strong minimality (7.9).- 8. Power Automata.- construction of power automata (8.2); power automata theorem (8.38.4); kernel automata (8.5).- 9. Initial Automata.- systematic of initial automata (9.2); free realization (9.3); minimal rl“*