**:** . .
**:**
**. :** 04200900023/0004

**:** 24
**:**
**:** 2009
**:** . . / . 24. .: , 2009. .81-98.

** :** , ,

** (.):** finite state machine, phase picture of the discrete determined dynamic system, estimation of complexity

**:** (), - . : , , , , , , , , .. , , .

** (.):** Operations rules are analyzed of the discrete determined dynamic systems (finite state machine) presented in the form of geometrical images - schedules with numerical coordinates of points. As geometrical images are considered classical geometrical curves: golden spiral, Lemniscate of Bernouilli, a ballistic curve,Equiangular spiral, Archimedian spiral, Astroid, Galileo's spiral, Brachistochrone (or brachistochronous) curve etc. In article is researched dependence of number of conditions at the minimal finite state machine constructed on a curve, from power of the entrance alphabet of the finite state machine.

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