P systems with evolutional symport and membrane creation rules solving QSAT

Orellana-Martín, David; Valencia-Cabrera, Luis; Pérez–Jiménez, Mario J.

doi:10.1016/j.tcs.2021.11.012

Cited by 4 publications

(8 citation statements)

References 24 publications

(29 reference statements)

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“…Remark 1 One can notice that the number of pairs generated above is N * (N/2+1)/4 which is less than the number of pairs, N 2 , used in previous solutions [29][30][31].…”

Section: Unary Encodingmentioning

confidence: 91%

“…In the context of membrane computing, any solution to an NP-Hard problem has to have an underlying exponential space support. As exemplified by articles [30] and [34] there are two different approaches/philosophies:…”

Section: Solutions To Integer Factorisation Problemmentioning

confidence: 99%

“…So, the space complexity of both solutions is O( √ N ). The time complexity The compartment C 2,1 with configuration M 1,0 = x ⋆1,0 y ⋆1,0 p ⋆1,0 z ⋆1,0 δ 1,0 , where x ⋆1,0 = x 0 , y ⋆1,0 = y 0 , p ⋆1,0 = p 0 , z ⋆1,0 = λ, δ 1,0 = rP n N ⋆ reported in [29] is O(k * logk) and in [30] is O(k), whereas the space complexity is O(N 2 ) for both of them.…”

Section: Complexitymentioning

confidence: 99%

“…In article [29] the authors offer a solution to the integer factorisation problem, using polarization P systems with active membranes. In [30] it is provided a solution to the integer factorisation problem based on polarizationless P systems, to generate all pairs of numbers P and Q, using partial functions from N to N 2 such that their product is equal to N . In [31] an asynchronous P system model is used in order to provide a solution to the factorisation problem.…”

Section: Introductionmentioning

confidence: 99%

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Breaking RSA Encryption Protocol with Kernel P Systems

Vasile

Gheorghe

Niculescu

2023

Preprint

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The prime factorisation problem is intractable, i.e., no efficient algorithm is known. In cryptography there are some well-known approaches based on the computational hardness of this problem, including Rivest-Shamir-Adleman (RSA) encryption protocol. Several attemps to break RSA have been investigated, some of them based on the massive parallelism of membrane systems.In this paper a new approach, based on kernel P system formalism, aimed at reassessing the space-time tradeoff, usually involved in membrane computing solutions, is investigated. Two models are introduced and assessed in order to find the potential benefits of each of them for solving the above problem, revealing also their limitations and providing hints for further improvements.

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“…Remark 1 One can notice that the number of pairs generated above is N * (N/2+1)/4 which is less than the number of pairs, N 2 , used in previous solutions [29][30][31].…”

Section: Unary Encodingmentioning

confidence: 91%

Section: Solutions To Integer Factorisation Problemmentioning

confidence: 99%

Section: Complexitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Breaking RSA Encryption Protocol with Kernel P Systems

Vasile

Gheorghe

Niculescu

2023

Preprint

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“…In the framework of cell-like membrane systems, creation rules have been used lately besides evolutional communication rules in [12] to solve the SAT problem by means of a family of recognizer P systems with evolutional communication rules and creation rules. In [13], an efficient solution to QSAT is given by means of a family of recognizer polarizationless P systems with active membranes and membrane creation, and in [14], an efficient solution to QSAT is given by means of a family of P systems with evolutional symport/antiport rules of length (1, 1) and creation rules. Creation rules have not been used in P systems with classical symport/antiport rules.…”

Section: Introductionmentioning

confidence: 99%

Membrane creation and symport/antiport rules solving QSAT

2022

Self Cite

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In Membrane Computing, different variants of devices can be found by changing both syntactical and semantic ingredients. These devices are usually called membrane systems or P systems, and they recall the structure and behavior of living cells in the nature. In this sense, rules are introduced as a way for objects to interact with membranes, giving P systems the ability to solve computational problems. Some of these rules, as division, separation and creation rules are inspired by the membrane division through the mitosis process or new membranes are created through gemmation. These rules seem to be crucial in the path to solve computationally hard problems. In this work, creation rules are used in classical P systems with symport/antiport rules, where objects travel through membranes without changing to achieve enough computational power to efficiently solve PSPACE-complete problems. More precisely, a solution to the problem is given by means of a uniform family of these systems. This paper was originally submitted to the International Conference on Membrane Computing 2021.

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