Aperiodic pseudorandom number generators based on infinite words

Balkova, Lubomira; Bucci, Michelangelo; Luca, Alessandro De; Hladký, Jiří; Puzynina, Svetlana

doi:10.1016/j.tcs.2016.07.042

Cited by 11 publications

(30 citation statements)

References 13 publications

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“…the type SS, cannot appear. We can prove this using the results from [2]. It also follows from the proof of Theorem 4 in [30].…”

Section: Return Words To Prefixes Of Complementary Symmetric Rote Seqmentioning

confidence: 77%

“…As shown in [2], all Sturmian sequences have the WELLDOC(2) property. Let us suppose that w is a prefix of u with two stable return words, i.e.…”

Section: Return Words To Prefixes Of Complementary Symmetric Rote Seqmentioning

confidence: 98%

“…Thus w (2) originates in u (2) with the directive sequence bbβbbβ · · · . The return words to w (2) are ϕ b ϕ β (0) = 010 and ϕ b ϕ β (1) = 01 and its derivated sequence is d u (w (2) ) = d u (2) (ε) = u (2) .…”

Section: Types Of Bispecial Prefixes Of Sturmian Sequencesmentioning

confidence: 99%

“…For the bispecial prefix w (2) we have z 0 z 1 = bβ and z 2 z 3 z 4 · · · = bbβb · · · has the prefix b 2 β. Therefore its matrix is…”

Section: Types Of Bispecial Prefixes Of Sturmian Sequencesmentioning

confidence: 99%

“…After that we move along the edge labelled by ϕ b to the vertex 0 1 1 1 . This vertex is the desired matrix P (2) .…”

Section: Types Of Bispecial Prefixes Of Sturmian Sequencesmentioning

confidence: 99%

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Derived sequences of complementary symmetric Rote sequences

Medková

Pelantová

Vuillon

2019

RAIRO-Theor. Inf. Appl.

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Complementary symmetric Rote sequences are binary sequences which have factor complexity C(n) = 2n for all integers n ≥ 1 and whose languages are closed under the exchange of letters. These sequences are intimately linked to Sturmian sequences. Using this connection we investigate the return words and the derivated sequences to the prefixes of any complementary symmetric Rote sequence v which is associated with a standard Sturmian sequence u. We show that any non-empty prefix of v has three return words. We prove that any derivated sequence of v is coding of three interval exchange transformation and we determine the parameters of this transformation. We also prove that v is primitive substitutive if and only if u is primitive substitutive. Moreover, if the sequence u is a fixed point of a primitive morphism, then all derivated sequences of v are also fixed by primitive morphisms. In that case we provide an algorithm for finding these fixing morphisms.

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“…the type SS, cannot appear. We can prove this using the results from [2]. It also follows from the proof of Theorem 4 in [30].…”

Section: Return Words To Prefixes Of Complementary Symmetric Rote Seqmentioning

confidence: 77%

“…As shown in [2], all Sturmian sequences have the WELLDOC(2) property. Let us suppose that w is a prefix of u with two stable return words, i.e.…”

Section: Return Words To Prefixes Of Complementary Symmetric Rote Seqmentioning

confidence: 98%

Section: Types Of Bispecial Prefixes Of Sturmian Sequencesmentioning

confidence: 99%

“…For the bispecial prefix w (2) we have z 0 z 1 = bβ and z 2 z 3 z 4 · · · = bbβb · · · has the prefix b 2 β. Therefore its matrix is…”

Section: Types Of Bispecial Prefixes Of Sturmian Sequencesmentioning

confidence: 99%

“…After that we move along the edge labelled by ϕ b to the vertex 0 1 1 1 . This vertex is the desired matrix P (2) .…”

Section: Types Of Bispecial Prefixes Of Sturmian Sequencesmentioning

confidence: 99%

See 3 more Smart Citations

Derived sequences of complementary symmetric Rote sequences

Medková

Pelantová

Vuillon

2019

RAIRO-Theor. Inf. Appl.

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Lie hypergraph and chaos‐based privacy preserving protocol for wireless sensor networks in IoT environment

Sridharan,

Rajendran,

Venkatraman

2023

Int J Communication

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SummaryWireless sensor networks (WSN) are innately resource restrained and beneficial in a wide range of applications, including smart homes, e‐health care, law, military systems, disaster management, and emergency reprieve. These applications are linked to various devices that may communicate with one another through the internet, typically known as Internet of Things (IoT). The application of WSN plays an integral role in the IoT infrastructure. In a WSN, sensors are haphazardly placed in environments where the data transmission is challenged by privacy concerns. This paper proposes a methodology termed Lie hypergraph and chaos‐based secure routing (LH‐CSR) to perform an energy‐efficient routing with secure data transmission in WSN. In the first phase, the deployed sensor nodes are transformed into a hypergraph from which cluster head (CH) is elected by hypergraph transversal property, and for secure routing, the route is formed by the Lie commutators of the Lie algebra of upper triangular matrices. The second phase emphasizes privacy preservation by introducing the novel chaotic map formulation to process the key generation. The encryption and decryption processes are maintained by key generation to prevent data loss during retrieval. In this way, the data are retained confidentially with minimal computational overhead. The performance of the LH‐CSR is evaluated through a simulation, which shows that it outperforms over compared protocols in terms of cryptographic time, network lifetime, packet delivery ratio, end‐to‐end delay, and throughput.

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On Balanced Sequences and Their Asymptotic Critical Exponent

Dolce

Dvorakova

Pelantová

2021

Language and Automata Theory and Applications

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We study aperiodic balanced sequences over finite alphabets. A sequence v of this type is fully characterised by a Sturmian sequence u and two constant gap sequences y and y ′ . We show that the language of v is eventually dendric and we focus on return words to its factors. We deduce a method computing critical exponent and asymptotic critical exponent of balanced sequences provided the associated Sturmian sequence u has a quadratic slope. The method is based on looking for the shortest return words to bispecial factors in v. We illustrate our method on several examples, in particular we confirm a conjecture of Rampersad, Shallit and Vandomme that two specific sequences have the least critical exponent among all balanced sequences over 9-resp. 10-letter alphabets.

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Aperiodic pseudorandom number generators based on infinite words

Cited by 11 publications

References 13 publications

Derived sequences of complementary symmetric Rote sequences

Derived sequences of complementary symmetric Rote sequences

Lie hypergraph and chaos‐based privacy preserving protocol for wireless sensor networks in IoT environment

On Balanced Sequences and Their Asymptotic Critical Exponent

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