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Parametric Iteration in Resource Theories

Authors Alessandro Di Giorgio , Pawel Sobocinski , Niels Voorneveld

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LIPIcs.CSL.2026.29.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Program semantics
  • Theory of computation → Logic and verification
  • Mathematics of computing → Probability and statistics
Keywords
  • Markov categories
  • Cryptography
  • String diagrams
  • Asymptotic equivalence

Metrics

Abstract

Many algorithms are specified with respect to a fixed but unknown parameter. Examples of this are especially common in cryptography, where protocols often feature a security parameter such as the bit length of a secret key.
Our aim is to capture this phenomenon in a more abstract setting. We focus on resource theories - general calculi of processes with a string diagrammatic syntax - introducing a general parametric iteration construction. By instantiating this construction within the Markov category of probabilistic Boolean circuits and equipping it with a suitable metric, we are able to capture the notion of negligibility via asymptotic equivalence, in a compositional way. This allows us to use diagrammatic reasoning to prove simple cryptographic theorems - for instance, proving that guessing a randomly generated key has negligible success.

Cite As Get BibTex

Alessandro Di Giorgio, Pawel Sobocinski, and Niels Voorneveld. Parametric Iteration in Resource Theories. In 34th EACSL Annual Conference on Computer Science Logic (CSL 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 363, pp. 29:1-29:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.CSL.2026.29

Author Details

Alessandro Di Giorgio
  • Tallinn University of Technology, Estonia
Pawel Sobocinski
  • Tallinn University of Technology, Estonia
Niels Voorneveld
  • Cybernetica AS, Tartu, Estonia

Funding

Di Giorgio, Voorneveld and Sobocinski were supported by the European Union under Grant Agreement No. 101087529. Sobocinski was additionally supported by the Estonian Research Council via grants PRG1215 and TEM-TA5 and the Estonian Center of Excellence in Artificial Intelligence (EXAI).

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