insight - Formal language theory

### Compiling Temporal Counting Logic into Softmax Transformers

Temporal counting logic Kt[#] and its equivalent RASP variant C-RASP are the best-known lower bound on the expressivity of future-masked softmax transformer encoders.

### Commutative N-polyregular Functions: Decidability and Characterization

Commutative N-polyregular functions can be effectively characterized and their membership is decidable. This resolves an open conjecture on the relationship between star-free N-polyregular functions and star-free Z-polyregular functions.

### Transformers as Formal Transducers: Expressivity and Limits

Transformers can express surprisingly large classes of string-to-string transductions, including first-order rational, regular, and polyregular functions, which can be simulated using variants of the RASP programming language.

### Universality of Regular Realizability Problems for Finite Relations

The paper proves the universality of regular realizability problems for several classes of finite relations on the set of non-negative integers, where the relations are described in a specific format. The universality is shown up to reductions using NP-oracles.