Geometrical abstract automata. (English) Zbl 0656.68059

Huckenbeck, Ulrich

Computational geometry and its applications, Proc. Int. Workshop, Würzburg/FRG 1988, Lect. Notes Comput. Sci. 333, 217-231 (1988).

[For the entire collection see Zbl 0651.00016.]
The author presents a survey of his thesis work [Geometrische Maschinenmodelle, Diss. Würzburg (1986; Zbl 0642.68102)] which deals with automata whose basis operations are geometric (join and intersection for points, lines, and circles.) He deals with the problems presented by the non uniqueness of intersection points generated by circles and notes that geometrically this indetermination appears in all problems that cannot be solved by rational functions. The paper also contains statements of some decidability and complexity of computation statements.

Reviewer: H.Guggenheimer

MSC:

68Q45	Formal languages and automata
51M15	Geometric constructions in real or complex geometry

Keywords:

geometrical abstract automata; intersection points; decidability; complexity