Properties of Right One-Way Jumping Finite Automata.

Right one-way jumping finite automata (ROWJFAs), were recently introduced in H. Chigahara et al. (2016) [3] 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 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 families of the Chomsky-hierarchy and related families. We also give more characterizations of languages accepted by ROWJFAs in the case that the language is given as the concatenation of two languages.