Watson-Crick Jumping Finite Automata
16 Nov 2020-Vol. 31, Iss: 07, pp 467-480
TL;DR: This paper introduces a new automata called Watson-Crick jumping finite automata, working on tapes which are double stranded sequences of symbols, similar to that of a Watson- Crick automata.
Abstract: In this paper, we introduce a new automata called Watson-Crick jumping finite automata, working on tapes which are double stranded sequences of symbols, similar to that of a Watson-Crick automata. This automata scans the double stranded sequence in a discontinuous manner (i.e.) after reading a double stranded string, the automata can jump over some subsequence and continue scanning, depending on the rule. We define some variants of such automata and compare the languages accepted by these variants with the language classes in Chomsky hierarchy. We also investigate some closure properties.
Citations
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TL;DR: The accepting power of the new model of Watson–Crick finite automata is studied and compared with the original models and also other well-known language families, and a comprehensive hierarchy of all related language families is presented.
1 citations
01 Jan 1982
TL;DR: This note provides a sufficient condition for a copy language to be regular; an application of this condition is demonstrated.
Abstract: Abstract Let Σ be an arbitrary fixed alphabet. The direct copying relation (over Σ+) is a binary relation defined by: x copy y if and only if x = x1ux2 and y = x1uux2 for some words x1,x2,u where u is nonempty. The copying relation copy∗ is defined as the reflexive and transitive closure of copy. A copying system is an ordered pair G = (Σ, w) where w ϵΣ+; its language is L(G) = {zϵΣ + : w copy ∗ z} , it is referred to as a copy language. This note provides a sufficient condition for a copy language to be regular; an application of this condition is demonstrated.
1 citations
1 citations
08 Mar 2023
TL;DR: In this article , the Szilard control languages of a new type of computing model where the underlying model is based on the working of DNA molecules are investigated and compared with the family of control languages such as REG, CF and RE.
Abstract: DNA molecules are the building blocks of life. In the last few decades, the fields of biotechnology and molecular biology have made significant progress. Computer scientists have used the storage capacity and massive parallelism of DNA molecules in order to build computing devices and investigated the computing powers of these models and their efficiency in solving computational hard problems. In this paper, we investigate Szilard / control languages of a new type of computing model where the underlying model is based on the working of DNA molecules. DNA molecules are double-stranded and contain chains of nucleotides. These nucleotides are characterized into four types, i.e., A (adenine), T (thymine), G (guanine) and C (cytosine) based on their chemical bases. Furthermore, these nucleotides follow Watson-Crick complementary, i.e., A-T and G-C pairing. We derive the Szilard / control languages of Watson-crick (WK) grammars. Also, we compare the family of Szilard / control languages of these systems with the family of languages such as REG, CF and RE.
Posted Content•
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.
References
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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
26 Jun 2006
TL;DR: In this article, it was shown that the classes of the Chomsky hierarchy are closed under bounded duplication, where the factors duplicated cannot exceed a given length, and the class of context-free languages is closed under duplication over alphabets of any size.
Abstract: Duplication is an operation generating a language from a single word by iterated application of rewriting rules u →uu on factors. We extend this operation to entire languages and investigate, whether the classes of the Chomsky hierarchy are closed under duplication. Here we treat mainly bounded duplication, where the factors duplicated cannot exceed a given length.
While over two letters the regular languages are closed under bounded duplication, over three or more letters they are not, if the length bound is 4 or greater. For 2 they are closed under duplication, the case of 3 remains open. Finally, the class of context-free languages is closed under duplication over alphabets of any size.
18 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
Journal Article•
TL;DR: This work extends this operation to entire languages and investigates, whether the classes of the Chomsky hierarchy are closed under duplication, and treats mainly bounded duplication, where the factors duplicated cannot exceed a given length.
Abstract: Duplication is an operation generating a language from a single word by iterated application of rewriting rules u → uu on factors. We extend this operation to entire languages and investigate, whether the classes of the Chomsky hierarchy are closed under duplication. Here we treat mainly bounded duplication, where the factors duplicated cannot exceed a given length. While over two letters the regular languages are closed under bounded duplication, over three or more letters they are not, if the length bound is 4 or greater. For 2 they are closed under duplication, the case of 3 remains open. Finally, the class of context-free languages is closed under duplication over alphabets of any size.
15 citations
TL;DR: The class of languages defined by the iterated application of the prefix–suffix duplication to a word is considered and it is shown that such a language is context-free if and only if the initial word contains just one letter.
11 citations