A finite state automaton is adopted as a model for discrete event dynamic systems (DEDS). Observations are assumed to be a subset of the event alphabet. Observability is defined as having perfect knowledge of the current state at points in time separated by bounded numbers of transitions. A polynomial test for observability is given. It is shown that an observer may be constructed and implemented in polynomial time and space. A bound on the cardinality of the observer state space is also presented. A notion of resiliency is defined for observers, and a test for resilient observability and a procedure for the construction of a resilient observer are presented. >

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Observability of discrete event dynamic systems

This paper establishes a fundamental framework of automata theory based on complete residuated lattice-valued logic. First it deals with how to extend the transition relation of states and particularly presents a characterization of residuated lattice by fuzzy automata (called l valued automata). After that fuzzy subautomata (called l valued subautomata), successor and source operators are proposed and their basic properties as well as the equivalent relation among them are discussed, from which it follows that the two fuzzy operators are exactly fuzzy closure operators. Finally anL bifuzzy topological characterization of l valued automata is presented, so a more generalized fuzzy automata theory is built.

Automata theory based on complete residuated lattice-valued logic

Characterizations of fuzzy finite automata

On subsystems of a fuzzy finite state machine

Products of T -generalized state machines and T -generalized transformation semigroups

Introduction 1 Semigroups and their relatives 2 Machines and semigroups 3 Decompositions 4 The holonomy decomposition 5 Recognizers 6 Sequential machines and functions Appendix References Index of notation Index

William M. Holcombe

Papers

Algebraic automata theory