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As transformers have gained prominence in natural language processing, someresearchers have investigated theoretically what problems they can and cannotsolve, by treating problems as formal languages. Exploring questions such asthis will help to compare transformers with other models, and transformervariants with one another, for various tasks. Work in this subarea has madeconsiderable progress in recent years. Here, we undertake a comprehensivesurvey of this work, documenting the diverse assumptions that underliedifferent results and providing a unified framework for harmonizing seeminglycontradictory findings.

Transformers as Recognizers of Formal Languages: A Survey on Expressivity