Behaviorally Correct Language Identification.

Abstract: The concept of Behaviorally Correct (BC) language identification, is a paradigm in inductive 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 r1​> r, TxtBCr ​⊂ TxtBCr1, and similarly UBCr​ ⊂ UBCr1​​ and UTxtBCr ​⊂ UTxtBCr1, indicating that relaxation of error bounds yields 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.

computation and languageformal languages and automata theorymachine learninglogic

Audience: researchers in the topic

Online logic seminar

Series comments: Description: Seminar on all areas of logic