“…By allowing nondeterministic transitions (1nfas) or/and movements of the head in both directions on the input tape, so obtaining two-way deterministic and nondeterministic finite automata (2dfas/2nfas), the computational power does not increase [21,24]. Other extensions of finite automata have been proved to capture the same class of languages, such as constant-height pushdown automata [2,4], straight-line programs [2], 1-limited automata [28,18,19], or, as will be of interest for this work, linear-time one-tape Turing machines [8,20,5,6]. 1 A natural question concerning models that share the same computational power is the comparison of the sizes of their descriptions.…”