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Saturating right congruences. (English) Zbl 0716.68057

Table-transition automata are considered, related to Muller automata, for recognizing rational \(\omega\)-languages. The deterministic automata are mainly investigated, because they are isomorphic to a family of finite right congruences satisfying a property of saturation similar to those defined for congruences by A. Arnold [Lect. Notes Computer Sci. 192, 18-27 (1985; Zbl 0612.68073)] and J. R. Büchi (Proc. Internat. Congress on Logic, Methodology and Philosophy, Stanford Univ. Press, 1962, 1-11). Finally, a variant of the property used by L. H. Landweber [Math. Syst. Theory 3, 376-384 (1969)] for characterizing deterministic \(\omega\)-languages is given.
Reviewer: G.Paun

MSC:

68Q45 Formal languages and automata

Citations:

Zbl 0612.68073
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References:

[1] A. ARNOLD, Deterministic and non-anbiguous rational w-languages, L.N.C.S., 1984, n^\circ 192, pp. 18-27. Zbl0612.68073 MR814729 · Zbl 0612.68073
[2] J. R. BÜCHI, On a decision method in restricted second order arithmetic, Proc. Internat. Congress on Logic, Methodology and philosophy, Stanford Univ. Press, 1962, pp. 1-11. Zbl0147.25103 MR183636 · Zbl 0147.25103
[3] S. EILENBERG, Automata, Languages and Machines, Vol. A., Academic Press, 1974. Zbl0317.94045 MR530382 · Zbl 0317.94045
[4] L. H. LANDWEBER, Decision problems for w-automata, Math. Sys. Theor., 1969, 3, pp. 376-384. Zbl0182.02402 MR260595 · Zbl 0182.02402 · doi:10.1007/BF01691063
[5] B. LE SAEC, Thèse de doctorat. Étude de la reconnaissabilité des langages rationnels de mots infinis, 1986, n^\circ 85, Université de Bordeaux.
[6] R. MCNAUGHTON, Testing and generating infinité sequences by finite automaton. Information and control, 1966, n^\circ 9, pp. 521-530. Zbl0212.33902 MR213241 · Zbl 0212.33902 · doi:10.1016/S0019-9958(66)80013-X
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