Topologies for the set of disjunctive ω-words
An infinite sequence (ω-word) is referred to as disjunctive provided it contains every finite word as infix (factor). As Jürgensen and Thierrin [JT83] observed the set of disjunctive ω-words, D, has a trivial syntactic monoid but is not accepted by a finite automaton. In this paper we derive some to...
Elmentve itt :
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| Dokumentumtípus: | Cikk |
| Megjelent: |
2005
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| Sorozat: | Acta cybernetica
17 No. 1 |
| Kulcsszavak: | Számítástechnika, Kibernetika |
| Tárgyszavak: | |
| Online Access: | http://acta.bibl.u-szeged.hu/12752 |
| Tartalmi kivonat: | An infinite sequence (ω-word) is referred to as disjunctive provided it contains every finite word as infix (factor). As Jürgensen and Thierrin [JT83] observed the set of disjunctive ω-words, D, has a trivial syntactic monoid but is not accepted by a finite automaton. In this paper we derive some topological properties of the set of disjunctive ω-words. We introduce two non-standard topologies on the set of all ω-words and show that D fulfills some special properties with respect to these topologies. In the first topology - the so-called topology of forbidden words - D is the smallest nonempty Gδ-set, and in the second one D is the set of accumulation points of the whole space as well as of itself. |
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| Terjedelem/Fizikai jellemzők: | 43-51 |
| ISSN: | 0324-721X |