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Generalized Circular One-Way Jumping Finite Automata.
TL;DR: In this article, a generalized linear one-way jumping finite automata (GLone-way-jumping-finite automata) model was defined and compared with the original one.
Abstract: A new discontinuous model of computation called one-way jumping finite automata was defined by H. Chigahara et. al. This model was a restricted version of the model jumping finite automata. These automata read an input symbol-by-symbol and jump only in one direction. A generalized linear one-way jumping finite automaton makes jumps after deleting a substring of an input string and then changes its state. These automata can make sequence of jumps in only one direction on an input string either from left to right or from right to left. We show that newly defined model is powerful than its original counterpart. We define and compare the variants, generalized right linear one-way jumping finite automata and generalized left linear one-way jumping finite automata. We also compare the newly defined models with Chomsky hierarchy. Finally, we explore closure properties of the model.
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TL;DR: The paper establishes several results concerning jumping finite automata in terms of commonly investigated areas of automata theory, such as decidability and closure properties, and achieves several results that demonstrate differences between jumping finiteAutomata and classical finite Automata.
Abstract: The present paper proposes a new investigation area in automata theory — jumping finite automata. These automata work like classical finite automata except that they read input words discontinuously — that is, after reading a symbol, they can jump over some symbols within the words and continue their computation from there. The paper establishes several results concerning jumping finite automata in terms of commonly investigated areas of automata theory, such as decidability and closure properties. Most importantly, it achieves several results that demonstrate differences between jumping finite automata and classical finite automata. In its conclusion, the paper formulates several open problems and suggests future investigation areas.
77 citations
TL;DR: In this article, the authors characterize the corresponding class of languages in terms of special shuffle expressions and survey other equivalent notions from the existing literature, and present several results concerning computational hardness and algorithms for parsing and other basic tasks concerning jumping finite automata.
24 citations
TL;DR: The one-way jumping finite automaton model is proposed, restricting the jumping relation of the recently introduced jumping finite Automaton so that the machine can only jump over symbols it cannot process in its current state.
Abstract: We propose the one-way jumping finite automaton model, restricting the jumping relation of the recently introduced jumping finite automaton so that the machine can only jump over symbols it cannot process in its current state. The reading head of a one-way jumping finite automaton moves deterministically in one direction within the input word, whereas movement of the reading head of jumping finite automaton is non-deterministic. The class of languages accepted by one-way jumping finite automata is different from that of jumping finite automata, in particular, it includes all regular languages, as opposed to the latter. We study one-way jumping finite automata and obtain closure properties, a pumping lemma, and separation results with respect to the classical language classes of the Chomsky hierarchy.
22 citations
TL;DR: In this paper, the authors complete the initial study of jumping finite automata, which was started in a former article of Meduna and Zemek [7], and correct erroneous results presented in the article.
Abstract: We complete the initial study of jumping finite automata, which was started in a former article of Meduna and Zemek [7]. The open questions about basic closure properties are solved. Besides this, we correct erroneous results presented in the article. Finally, we point out important relations between jumping finite automata and some other models studied in the literature.
18 citations
10 Sep 2018
TL;DR: 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.
Abstract: We continue our investigation [S. Beier, M. Holzer: Properties of right one-way jumping finite automata. In Proc. 20th DCFS, number 10952 in LNCS, 2018] on (right) one-way jumping finite automata (ROWJFA), 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 also discuss some complexity results for the considered decision problems.
9 citations