Graph-Controlled Insertion-Deletion Systems

Freund, Rudolf; Kogler, Marian; Rogozhin, Yurii; Verlan, Sergey

doi:10.4204/eptcs.31.11

Cited by 32 publications

(18 citation statements)

References 15 publications

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“…We remark that our results for matrix insertion-deletion systems are different from the results on graph-controlled systems obtained in [4] and previous works. In the graph-controlled case, the total number of nodes in the graph is minimized, while in the matrix case the depth of the graph (corresponding to the size of matrices) is minimized.…”

Section: Discussioncontrasting

confidence: 99%

“…Such a formalization is rather similar to the definition of insertion-deletion P systems [19], however it is even simpler and more natural. The article [4] focuses on one-sided graph-controlled insertion-deletion systems where at most two symbols may be present in the description of insertion and deletion rules. This correspond to systems of size (1, 1, 0; 1, 1, 0), (1, 1, 0; 1, 0, 1), (1, 1, 0; 2, 0, 0), and (2, 0, 0; 1, 1, 0), where the first three numbers represent the maximal size of the inserted string and the maximal size of the left and right contexts, while the last three numbers represent the same information, but for deletion rules.…”

Section: Introductionmentioning

confidence: 99%

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Matrix insertion–deletion systems

Petre

Verlan²

2012

Theoretical Computer Science

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In this article, we consider for the first time the operations of insertion and deletion working in a matrix controlled manner. We show that, similarly as in the case of context-free productions, the computational power is strictly increased when using a matrix control: computational completeness can be obtained by systems with insertion or deletion rules involving at most two symbols in a contextual or in a context-free manner and using only binary matrices.

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Section: Discussioncontrasting

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Matrix insertion–deletion systems

Petre

Verlan²

2012

Theoretical Computer Science

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“…One of the important variants of ins-del systems is graph-controlled ins-del systems introduced in [5] and further studied in [9]. In such a system, the concept of a component is introduced and is associated with every insertion or deletion rule.…”

Section: Introductionmentioning

confidence: 99%

Descriptional Complexity of Graph-Controlled Insertion-Deletion Systems

Fernau¹,

Kuppusamy²,

Raman³

2016

Descriptional Complexity of Formal Systems

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We consider graph-controlled insertion-deletion systems and prove that the systems with sizes (i) (, 0) and (iii) (2; 2, 0, 0; 1, 1, 1) are computationally complete. Moreover, graphcontrolled insertion-deletion systems simulate linear languages with sizes (2; 2, 0, 1, 1, 0, 0), (2; 2, 1, 0; 1, 0, 0), (3; 1, 0, 1; 1, 0, 0), or (3; 1, 1, 0; 1, 0, 0). Simulations of metalinear languages are also studied. The parameters in the size (k; n, i , i ; m, j , j ) of a graph-controlled insertion-deletion system denote (from left to right) the maximum number of components, the maximal length of the insertion string, the maximal length of the left context for insertion, the maximal length of the right context for insertion; a similar list of three parameters concerning deletion follows.

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“…Insertion-Deletion systems were defined as formal models of computation based on these operations and have been widely studied in the literature, see, e.g., [17] [31] [33] [34] [30] [18] [5]. Insertion-deletion systems that are context-free [27], that have one sidedcontext [28] [23], and that are graph controlled [6] were also proposed. P -systems with insertion-deletion rules have been extensively studied in [22] [24] [2] [1] [7] [8].…”

Section: Introductionmentioning

confidence: 99%

A Formal Language Model of DNA Polymerase Enzymatic Activity

Enaganti

Kari

Kopecki

2015

Fundamenta Informaticae

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We propose and investigate a formal language operation inspired by the naturally occurring phenomenon of DNA primer extension by a DNA-template-directed DNA Polymerase enzyme. Given two DNA strings u and v, where the shorter string v (called primer) is Watson-Crick complementary and can thus bind to a substring of the longer string u (called template) the result of the primer extension is a DNA string that is complementary to a suffix of the template which starts at the binding position of the primer. The operation of DNA primer extension can be abstracted as a binary operation on two formal languages: a template language L 1 and a primer language L 2 . We call this language operation L 1 -directed extension of L 2 and study the closure properties of various language classes, including the classes in the Chomsky hierarchy, under directed extension. Furthermore, we answer the question under what conditions can a given language of target strings be generated from a given template language when the primer language is unknown. We use the canonic inverse of directed extension in order to obtain the optimal solution (the minimal primer language) to this question.

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Graph-Controlled Insertion-Deletion Systems

Cited by 32 publications

References 15 publications

Matrix insertion–deletion systems

Matrix insertion–deletion systems

Descriptional Complexity of Graph-Controlled Insertion-Deletion Systems

A Formal Language Model of DNA Polymerase Enzymatic Activity

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