Calude, C.S., Priese, L., Staiger, L.: "Disjunctive Sequences: An Overview"; CDMTCS Research Report 063, Auckland (1997) Home/Search Document Details and Download
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Automatic Forcing and Genericity: On the Diagonalization.. - Ambos-Spies, Busse (Correct)
....characterization: A set A is bounded reg generic if and only if every binary word occurs in the characteristic sequence of A. Sequences with the latter property which we call saturated have been extensively studied in the literature under various names like rich or disjunctive (see e.g. [CPS97], He96] JT88] St76] St98] St01] We use this characterization to show that no bounded reg generic set is regular but that there are such generic sets which are context free, in fact linear. Moreover, we conclude that there are bounded reg generic sets which are not (bi )immune for the ....
....F = S has the required property. iii) i) Assume that M = S; s 0 ; F ) accepts Pre x( Then the 1 labelled automaton M = S; s 0 ; with (s) 1 if (s; 1) 2 F 0 otherwise computes a total function f such that f( n) n) for n 0. 5 As Calude et al. [CPS97] have observed, a pre x set is regular if and only if it is context free. So in the above theorem we may replace (iii) by the condition that the pre x set Pre x( of is context free. Regularity of a set and regularity of its characteristic sequence are related as follows. Theorem 2.2 If ....
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C. S. Calude, L. Priese and L. Staiger, Disjunctive sequences: an overview, CDMTCS Research Report 63, October 1997.
Topologies for the Set of Disjunctive omega-Words - Staiger (2001) Self-citation (Staiger) (Correct)
....of the language of all disjunctive sequences over X, D, and its topological 2 The term forbidden refers to the fact that closed subsets are specified by forbidding a certain set W of infixes. 6 Ludwig Staiger properties in Cantor space. Some of the results in this section are reported in [CPS97, St01]. As in [JST83, JT83] an word 2 X is called disjunctive provided T( X . Thus D = f : T( X g. From this definition we obtain D = w2X X wX : 3) Our next lemma shows that D is an example of a language which has a trivial finite syntactic congruence but ....
C. Calude, L. Priese and L. Staiger, Disjunctive Sequences: An Overview, CDMTCS Research Report 063, 1997.
How Large is the Set of Disjunctive Sequences? - Staiger (2002) (Correct)
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Calude, C.S., Priese, L., Staiger, L.: "Disjunctive Sequences: An Overview"; CDMTCS Research Report 063, Auckland (1997)
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