One-Tape Turing Machine Variants and Language Recognition

We present two restricted versions of one-tape Turing machines. Both characterize the class of context-free languages. In the first version, proposed by Hibbard in 1967 and called limited automata, each tape cell can be rewritten only in the first $d$ visits, for a fixed constant $d\geq 2$. Furthermore, for $d=2$ deterministic limited automata are equivalent to deterministic pushdown automata, namely they characterize deterministic context-free languages. Further restricting the possible operations, we consider strongly limited automata. These models still characterize context-free languages. However, the deterministic version is less powerful than the deterministic version of limited automata. In fact, there exist deterministic context-free languages that are not accepted by any deterministic strongly limited automaton.Comment: 20 pages. This article will appear in the Complexity Theory Column of the September 2015 issue of SIGACT New

Multi-Head Finite Automata: Characterizations, Concepts and Open Problems

Multi-head finite automata were introduced in (Rabin, 1964) and (Rosenberg, 1966). Since that time, a vast literature on computational and descriptional complexity issues on multi-head finite automata documenting the importance of these devices has been developed. Although multi-head finite automata are a simple concept, their computational behavior can be already very complex and leads to undecidable or even non-semi-decidable problems on these devices such as, for example, emptiness, finiteness, universality, equivalence, etc. These strong negative results trigger the study of subclasses and alternative characterizations of multi-head finite automata for a better understanding of the nature of non-recursive trade-offs and, thus, the borderline between decidable and undecidable problems. In the present paper, we tour a fragment of this literature

On non-recursive trade-offs between finite-turn pushdown automata

It is shown that between one-turn pushdown automata (1-turn PDAs) and deterministic finite automata (DFAs) there will be savings concerning the size of description not bounded by any recursive function, so-called non-recursive tradeoffs. Considering the number of turns of the stack height as a consumable resource of PDAs, we can show the existence of non-recursive trade-offs between PDAs performing k+ 1 turns and k turns for k >= 1. Furthermore, non-recursive trade-offs are shown between arbitrary PDAs and PDAs which perform only a finite number of turns. Finally, several decidability questions are shown to be undecidable and not semidecidable