Input-Erasing Two-Way Finite Automata
Alexander Meduna, Dominik Nejedlý, Zbyněk Křivka
TL;DR
This work introduces input-erasing two-way finite automata (IETWFA), which erase each read input symbol and can start at any position on the input tape. It proves that IETWFA characterize the class of $linear\ languages$, strictly larger than regular languages, by establishing bidirectional translations with linear grammars: for every $M$ there is a $G$ with $L(G)=L(M)$ and vice versa, including ε-free versions. The paper further explores restricted variants (e.g., even/init-even computations) and input-restriction scenarios, showing how these relate to $ELG$ and $LG$, sometimes reducing power to regular languages or finite automata. Collectively, the results build a robust bridge between erasing, two-way automata and linear grammars, with several open problems in determinism, minimization, and extended input-restriction frameworks.
Abstract
The present paper introduces and studies an alternative concept of two-way finite automata called input-erasing two-way finite automata. Like the original model, these new automata can also move the reading head freely left or right on the input tape. However, each time they read a symbol, they also erase it from the tape. The paper demonstrates that these automata define precisely the family of linear languages and are thus strictly stronger than the original ones. Furthermore, it introduces a variety of restrictions placed upon these automata and the way they work and investigates the effect of these restrictions on their acceptance power. In particular, it explores the mutual relations of language families resulting from some of these restrictions and shows that some of them reduce the power of these automata to that of even linear grammars or even ordinary finite automata.