Right one-way jumping finite automata (ROWJFAs), were recently introduced in [H. Chigahara, S. Z. Fazekas, A. Yamamura: One-Way Jumping Finite Automata, Internat. J. Found. Comput. Sci., 27(3), 2016] and are jumping automata that process the input in a discontinuous way with the restriction that the input head reads deterministically from left-to-right starting from the leftmost letter in the input and when it reaches the end of the input word, it returns to the beginning and continues the computation. We solve most of the open problems of these devices. In particular, we characterize the family of permutation closed languages accepted by ROWJFAs in terms of Myhill-Nerode equivalence classes. Using this, we investigate closure and non-closure properties as well as inclusion relations to other language families. We also give more characterizations of languages accepted by ROWJFAs for some interesting cases.

We continue our investigation [S. Beier, M. Holzer: Properties of right one-way jumping finite automata. In Proc. [Formula: see text]th DCFS, LNCS, 2018] on (right) one-way jumping finite automata (ROWJFAs), a variant of jumping automata, which is an automaton model for discontinuous information processing. Here we focus on decision problems for ROWJFAs. It turns out that most problems such as, e.g., emptiness, finiteness, universality, the word problem and variants thereof, closure under permutation, etc., are decidable. Moreover, we show that the containment of a language within the strict hierarchy of ROWJFA permutation closed languages induced by the number of accepting states as well as whether permutation closed regular or jumping finite automata languages can be accepted by ROWJFAs is decidable, too. On the other hand, we prove that for (linear) context-free languages the corresponding ROWJFA acceptance problem becomes undecidable. Moreover, we discuss also some complexity results for the considered decision problems.

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We consider jumping finite automata and their operational state complexity and decidability status. Roughly speaking, a jumping automaton is a finite automaton with a non-continuous input. This device has nice relations to semilinear sets and thus to Parikh images of regular sets, which will be exhaustively used in our proofs. In particular, we prove upper bounds on the intersection and complementation. The latter result on the complementation upper bound answers an open problem from [G. J. Lavado, G. Pighizzini, S. Seki: Operational State Complexity of Parikh Equivalence, 2014]. Moreover, we correct an erroneous result on the inverse homomorphism closure. Finally, we also consider the decidability status of standard problems as regularity, disjointness, universality, inclusion, etc. for jumping finite automata.