Finite Automata as Time-Inv Linear Systems Observability, Reachability and More

Authors:
Radu Grosu
Affiliations:
Department of Computer Science, Stony Brook University, Stony Brook, USA NY 11794-4400
Venue:
HSCC '09 Proceedings of the 12th International Conference on Hybrid Systems: Computation and Control
Year:
2009

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Abstract

We show that regarding finite automata (FA) as discrete, time-invariant linear systems over semimodules, allows to: (1) express FA minimization and FA determinization as particular observability and reachability transformations of FA, respectively; (2) express FA pumping as a property of the FA's reachability matrix; (3) derive canonical forms for FAs. These results are to our knowledge new, and they may support a fresh look into hybrid automata properties, such as minimality. Moreover, they may allow to derive generalized notions of characteristic polynomials and associated eigenvalues, in the context of FA.