We introduce and investigate forgetting 1-limited automata, which are
single-tape Turing machines that, when visiting a cell for the first time,
replace the input symbol in it by a fixed symbol, so forgetting the original
contents. These devices have the same computational power as finite automata,
namely they characterize the class of regular languages. We study the cost in
size of the conversions of forgetting 1-limited automata, in both
nondeterministic and deterministic cases, into equivalent one-way
nondeterministic and deterministic automata, providing optimal bounds in terms
of exponential or superpolynomial functions. We also discuss the size
relationships with two-way finite automata. In this respect, we prove the
existence of a language for which forgetting 1-limited automata are
exponentially larger than equivalent minimal deterministic two-way automata.Comment: In Proceedings NCMA 2023, arXiv:2309.0733