Codes1

Jürgensen, Helmut; Konstantinidis, Stavros

doi:10.1007/978-3-642-59136-5_8

Cited by 78 publications

(39 citation statements)

References 73 publications

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“…Statements of this type with L being regular have been obtained for various code-related properties and are of particular interest in the theory of codes [12]. In our case it is also interesting to note that the language L is not necessarily regular.…”

Section: Notementioning

confidence: 86%

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Bond-Free Languages: Formalizations, Maximality and Construction Methods

2005

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Abstract. The problem of negative design of DNA languages is addressed, that is, properties and construction methods of large sets of words that prevent undesired bonds when used in DNA computations. We recall a few existing formalizations of the problem and then define the property of sim-bond-freedom, where sim is a similarity relation between words. We show that this property is decidable for context-free languages and polynomial-time decidable for regular languages. The maximality of this property also turns out to be decidable for regular languages and polynomial-time decidable for an important case of the Hamming similarity. Then we consider various construction methods for Hamming bond-free languages, including the recently introduced method of templates, and obtain a complete structural characterization of all maximal Hamming bond-free languages. This result is applicable to the θ-k-code property introduced by Jonoska and Mahalingam.

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Section: Notementioning

confidence: 86%

“…In [9], the authors introduce the concept of a strictly τ -free code K, which is a generalization of the notion of comma-free code [12], and show that the language K + must be strictly τ -free as well. Here we shall assume that K is of fixed length k. In this formalization the tube language L is equal to K + .…”

Section: P1[k]mentioning

confidence: 99%

Bond-Free Languages: Formalizations, Maximality and Construction Methods

2005

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“…A code property, or independence, [15], is a set P of languages for which there is n ∈ N ∪ {ℵ 0 } such that L ∈ P, if and only if L ∈ P, for all L ⊆ L with 0 < |L | < n. If L is in P then we say that L satisfies P. Thus, L satisfies P exactly when all nonempty subsets of L with less than n elements satisfy P. A language L ∈ P is called P-maximal, or a maximal P code, if L ∪ {w} / ∈ P for any word w / ∈ L. We note that every L satisfying P is included in a maximal P code [15]. As far as we know, all code related properties in the literature [4,6,8,11,15,23,28] are code properties as defined here. The focus of this work is on 3-independences that can also be viewed as independences with respect to a binary relation in the sense of [29].…”

Section: Terminology and Backgroundmentioning

confidence: 99%

“…(f ) All the above classes and methods are open source (GPL). Our work is founded on independence theory [15,29] as well as the theory of rational relations and transducers [3,26].…”

Section: Introductionmentioning

confidence: 99%

Implementation of Code Properties via Transducers

Konstantinidis¹,

Meijer²,

Moreira

et al. 2016

Implementation and Application of Automata

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Abstract. The FAdo system is a symbolic manipulator of formal language objects, implemented in Python. In this work, we extend its capabilities by implementing methods to manipulate transducers and we go one level higher than existing formal language systems and implement methods to manipulate objects representing classes of independent languages (widely known as code properties). Our methods allow users to define their own code properties and combine them between themselves or with fixed properties such as prefix codes, suffix codes, error detecting codes, etc. The satisfaction and maximality decision questions are solvable for any of the definable properties. The new online system LaSer allows one to query about a code property and obtain the answer in a batch mode. Our work is founded on independence theory as well as the theory of rational relations and transducers, and contributes with improved algorithms on these objects.

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“…That is, for any two words w 1 , w 2 ∈ L such that w 1 = w 2 , we have w 1 p w 2 . For more detailed information on prefix codes we refer to [6].…”

Section: Corollary 5 Deterministic Watson-crick Automata Are Equivalmentioning

confidence: 99%

Descriptional Complexity of Formal Systems

2014

Lecture Notes in Computer Science

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Abstract. Watson-Crick automata are finite state automata working on double-stranded tapes, introduced to investigate the potential of DNA molecules for computing. In this paper, we continue the investigation of descriptional complexity of Watson-Crick automata initiated in [9]. In particular, we show that any finite language as well as any unary regular language can be recognized by a Watson-Crick automaton with only two and respectively three states. Also, we formally define the notion of determinism for these systems. Contrary to the case of non-deterministic Watson-Crick automata, we show that for deterministic ones, the complementarity relation plays a major role in the acceptance power of these systems.

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Codes1

Cited by 78 publications

References 73 publications

Bond-Free Languages: Formalizations, Maximality and Construction Methods

Bond-Free Languages: Formalizations, Maximality and Construction Methods

Implementation of Code Properties via Transducers

Descriptional Complexity of Formal Systems

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