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

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.

• Type: Conference
• Year: 2009
• Where: HYBRID
• Authors: Radu Grosu
• Keywords: Express Fa, Express Fa Minimization, FA’s Reachability Matrix, HYBRID 2009, Hybrid Systems