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An Additively Optimal Interpreter for Approximating Kolmogorov Prefix Complexity

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Τίτλος: An Additively Optimal Interpreter for Approximating Kolmogorov Prefix Complexity
Συγγραφείς: Zoe Leyva-Acosta, Eduardo Acuña Yeomans, Francisco Hernandez-Quiroz
Πηγή: Entropy, Vol 26, Iss 9, p 802 (2024)
Στοιχεία εκδότη: MDPI AG
Έτος έκδοσης: 2024
Συλλογή: Directory of Open Access Journals: DOAJ Articles
Θεματικοί όροι: algorithmic complexity, Kolmogorov complexity, coding theorem method, complexity approximation, Science, Astrophysics, QB460-466, Physics, QC1-999
Περιγραφή: We study practical approximations of Kolmogorov prefix complexity ( K ) using IMP2, a high-level programming language. Our focus is on investigating the optimality of the interpreter for this language as the reference machine for the Coding Theorem Method (CTM). This method is designed to address applications of algorithmic complexity that differ from the popular traditional lossless compression approach based on the principles of algorithmic probability. The chosen model of computation is proven to be suitable for this task, and a comparison to other models and methods is conducted. Our findings show that CTM approximations using our model do not always correlate with the results from lower-level models of computation. This suggests that some models may require a larger program space to converge to Levin’s universal distribution. Furthermore, we compare the CTM with an upper bound on Kolmogorov complexity and find a strong correlation, supporting the CTM’s validity as an approximation method with finer-grade resolution of K .
Τύπος εγγράφου: article in journal/newspaper
Γλώσσα: English
Relation: https://www.mdpi.com/1099-4300/26/9/802; https://doaj.org/toc/1099-4300; https://doaj.org/article/0a3aaae290604bf1b86c3aaab24147b6
DOI: 10.3390/e26090802
Διαθεσιμότητα: https://doi.org/10.3390/e26090802
https://doaj.org/article/0a3aaae290604bf1b86c3aaab24147b6
Αριθμός Καταχώρησης: edsbas.6CF554A6
Βάση Δεδομένων: BASE
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  – Url: https://doi.org/10.3390/e26090802#
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  Data: An Additively Optimal Interpreter for Approximating Kolmogorov Prefix Complexity
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  Data: <searchLink fieldCode="AR" term="%22Zoe+Leyva-Acosta%22">Zoe Leyva-Acosta</searchLink><br /><searchLink fieldCode="AR" term="%22Eduardo+Acuña+Yeomans%22">Eduardo Acuña Yeomans</searchLink><br /><searchLink fieldCode="AR" term="%22Francisco+Hernandez-Quiroz%22">Francisco Hernandez-Quiroz</searchLink>
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  Data: Entropy, Vol 26, Iss 9, p 802 (2024)
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  Data: MDPI AG
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  Data: 2024
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  Data: Directory of Open Access Journals: DOAJ Articles
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  Data: <searchLink fieldCode="DE" term="%22algorithmic+complexity%22">algorithmic complexity</searchLink><br /><searchLink fieldCode="DE" term="%22Kolmogorov+complexity%22">Kolmogorov complexity</searchLink><br /><searchLink fieldCode="DE" term="%22coding+theorem+method%22">coding theorem method</searchLink><br /><searchLink fieldCode="DE" term="%22complexity+approximation%22">complexity approximation</searchLink><br /><searchLink fieldCode="DE" term="%22Science%22">Science</searchLink><br /><searchLink fieldCode="DE" term="%22Astrophysics%22">Astrophysics</searchLink><br /><searchLink fieldCode="DE" term="%22QB460-466%22">QB460-466</searchLink><br /><searchLink fieldCode="DE" term="%22Physics%22">Physics</searchLink><br /><searchLink fieldCode="DE" term="%22QC1-999%22">QC1-999</searchLink>
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  Label: Description
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  Data: We study practical approximations of Kolmogorov prefix complexity ( K ) using IMP2, a high-level programming language. Our focus is on investigating the optimality of the interpreter for this language as the reference machine for the Coding Theorem Method (CTM). This method is designed to address applications of algorithmic complexity that differ from the popular traditional lossless compression approach based on the principles of algorithmic probability. The chosen model of computation is proven to be suitable for this task, and a comparison to other models and methods is conducted. Our findings show that CTM approximations using our model do not always correlate with the results from lower-level models of computation. This suggests that some models may require a larger program space to converge to Levin’s universal distribution. Furthermore, we compare the CTM with an upper bound on Kolmogorov complexity and find a strong correlation, supporting the CTM’s validity as an approximation method with finer-grade resolution of K .
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  Data: https://www.mdpi.com/1099-4300/26/9/802; https://doaj.org/toc/1099-4300; https://doaj.org/article/0a3aaae290604bf1b86c3aaab24147b6
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  Data: 10.3390/e26090802
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      – SubjectFull: algorithmic complexity
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      – SubjectFull: Kolmogorov complexity
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      – SubjectFull: coding theorem method
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            – TitleFull: Entropy, Vol 26, Iss 9, p 802 (2024
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