0000000000725618
AUTHOR
Raimonds Simanovskis
Closedness properties in ex-identification
In this paper we investigate in which cases unions of identifiable classes are also necessarily identifiable. We consider identification in the limit with bounds on mindchanges and anomalies. Though not closed under the set union, these identification types still have features resembling closedness. For each of them we and n such that (1) if every union of n − 1 classes out of U1, ... , Un is identifiable, so is the union of all n classes; (2) there are classes U1, ... ,Un−1 such that every union of n−2 classes out of them is identifiable, while the union of n − 1 classes is not. We show that by finding these n we can distinguish which requirements put on the identifiability of unions of cl…
Closedness Properties in EX-Identification of Recursive Functions
In this paper we investigate in which cases unions of identifiable classes of recursive functions are also necessarily identifiable. We consider identification in the limit with bounds on mindchanges and anomalies. Though not closed under the set union, these identification types still have features resembling closedness. For each of them we find such n that 1) if every union of n - 1 classes out of U1;, . . ., Un is identifiable, so is the union of all n classes; 2) there are such classes U1;, . . ., Un-1 that every union of n-2 classes out of them is identifiable, while the union of n - 1 classes is not. We show that by finding these n we can distinguish which requirements put on the iden…
Unions of identifiable classes of total recursive functions
J.Barzdin [Bar74] has proved that there are classes of total recursive functions which are EX-identifiable but their union is not. We prove that there are no 3 classes U1, U2, U3 such that U1∪U2,U1∪U3 and U2∪U3 would be in EX but U1∪U2∪U3∉ EX. For FIN-identification there are 3 classes with the above-mentioned property and there are no 4 classes U1, U2, U3, U4 such that all 4 unions of triples of these classes would be identifiable but the union of all 4 classes would not. For identification with no more than p minchanges a (2p+2−1)-tuple of such classes do exist but there is no (2p+2)-tuple with the above-mentioned properly.
Unions of identifiable families of languages
This paper deals with the satisfiability of requirements put on the identifiability of unions of language families. We consider identification in the limit from a text with bounds on mindchanges and anomalies. We show that, though these identification types are not closed under the set union, some of them still have features that resemble closedness. To formalize this, we generalize the notion of closedness. Then by establishing “how closed” these identification types are we solve the satisfiability problem.