Numeration-automatic sequences
J. F. J. Laros
Abstract
We present a base class of automata that induce a numeration system and we give an algorithm to give the n-th word in the language of the automaton when the expansion of n in the induced numeration system is feeded to the automaton. Furthermore we give some algorithms for reverse reading of this expansion and a way to combine automata to other automata having the same properties.
Create a lesson
Related papers
CritICL: Inference-Time Weak-to-Strong Generalization from Small Language Model Failure Modes
Yufan Wu, Yinghui He, Zhengyi Hu et al.
TTPO: Test-Time Policy Optimization
Aozhe Wang, Zhengxi Lu, Jianze Wang et al.
Stochastic Estimation of Transduced Language Models
Vésteinn Snæbjarnarson, Samuel Kiegeland, Manuel de Prada Corral et al.
Boosting LLM Exploration via Weak-Model Guidance in RLVR
Xingyu Shen, Huishuai Zhang, Peng Li et al.
Consolidating RLVR Capabilities Across Domains: A Deep Dive into Fusion Paradigms
Siye Wu, Kai Yang, Yuchen Cai et al.
How Language Models Organize and Structure Moral Knowledge
Orion Reblitz-Richardson