ASPECTS OF APPROXIMATE INDUCTIVE INFERENCE FOR BC LANGUAGE IDENTIFICATION

Author

Sunil Kumar Lal Karn, Southern Illinois University CarbondaleFollow

Date of Award

8-1-2025

Degree Name

Doctor of Philosophy

Department

Mathematics

First Advisor

Calvert, Wesley

Abstract

The concept of Behaviorally Correct (BC) language identification is a paradigm ininductive inference that allows learners to approximate target languages while tolerating a bounded density of errors. Beginning with foundational definitions, such as those of inductive inference machines (IIMs) and BC identification, we extend these notions to approximate identification using error densities and asymptotic uniform densities. Our results demonstrate the structured inclusion relations between various identification classes. Specifically, we prove that for any r, r1 ∈ [0, 1] with 0 ≤ r < r1 ≤ 1, T xtBCr ⊂ T xtBCr1, UT xtBCr ⊂ UT xtBCr1, and HUT xtBCr ⊂ HUT xtBCr1 indicating that relaxation of Error bounds yield strictly larger identification classes. Furthermore, leveraging the Operator Recursion Theorem, we construct examples demonstrating the non-equivalence of adjacent identification classes, highlighting the role of partial recursive functions in these separations. These results emphasize the versatility of BC identification frameworks in accommodating error densities while maintaining robust theoretical guarantees. Finally, we introduce uniform approximate BC identification and establish its utility in addressing local inconsistencies within language approximation, culminating in refined criteria that bridge global and local error bounds.