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The topological structure of adherences of regular languages. (English) Zbl 0608.68066
The topological structure of the adherences of regular languages is considered using zero-dimensional compact metric spaces, studied by {\it R. S. Pierce} [Mem. Am. Math. Soc. 130 (1972; Zbl 0253.54028)]. It is shown that the adherence of any regular language L is of such finite type, and from any automaton recognizing L a finite invariant structure, called a structural diagram by the author, is algorithmically constructible. This result implies that homeomorphism of adherences is decidable for regular languages. It is also shown that every zero- dimensional compact metrizable space of finite type is homeomorphic with the adherence of a regular language, where the language can be chosen to be two-testable in the strict sense.
Reviewer: M.Linna

MSC:
68Q45Formal languages and automata
54E45Compact (locally compact) metric spaces
WorldCat.org
Full Text: EuDML
References:
[1] 1. L. BOASSON and M. NIVAT, Adherences of Languages, Journal of Computer and System Sciences, Vol. 20, 1980, pp. 285-309. Zbl0471.68052 MR584863 · Zbl 0471.68052 · doi:10.1016/0022-0000(80)90010-0
[2] 2. T. HEAD, The Adherences of Languages as Topological Spaces, in: Automata on Infinite Wonds, edited by M. Nivat and D. Perrin, LNCS, vol. 192, Springer-Verlag, 1985. Zbl0571.68057 MR814740 · Zbl 0571.68057
[3] 3. J. G. HOCKING and G. S. YOUNG, Topology, Addison-Wesley, Reading, Mass., U.S.A., 1961. Zbl0135.22701 MR125557 · Zbl 0135.22701
[4] 4. R. MCNAUGHTON and S. PAPERT, Counter-Free Automata, M.I.T. Press, Cambridge, Mass., U.S.A., 1971. Zbl0232.94024 MR371538 · Zbl 0232.94024
[5] 5. R. S. PIERCE, Compact zero-dimensional metric spaces of finite type, Memoirs of the Amercan Mathematical Society, No. 130, Providence, Rhode Island, U.S.A., 1972. Zbl0253.54028 MR357268 · Zbl 0253.54028
[6] 6. S. WILLARD, General Topology, Addison-Wesley, Reading, Mass., U.S.A., 1970. Note added in proof: The following are recommended further references. Zbl0205.26601 MR264581 · Zbl 0205.26601
[7] R. LINDNER and L. STAIGER, Algebraische Codierungstheorie - Theorie der sequentiellen Codierungen, Akademie-Verlag, Berlin, 1977. Zbl0363.94016 MR469495 · Zbl 0363.94016
[8] L. STAIGER, Finite-state \omega -languages, J. Comput. System Sci. 27 (1983), pp. 434-448. Zbl0541.68052 MR727390 · Zbl 0541.68052 · doi:10.1016/0022-0000(83)90051-X