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ZENODO
Preprint . 2025
License: CC BY
Data sources: ZENODO
ZENODO
Preprint . 2025
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2025
License: CC BY
Data sources: Datacite
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Unifying Shannon Information Theory and Turing Computation Through Deterministic Representation

Authors: Kumar, Sanjay;

Unifying Shannon Information Theory and Turing Computation Through Deterministic Representation

Abstract

Shannon’s information theory and Turing’s theory of computation constitute the two foundational pillars of modern information and computation science. Shannon’s framework characterizes information in probabilistic terms-uncertainty, entropy, and compression-while Turing’s framework models computation as deterministic symbolic state evolution governed by fixed transition rules. Although deeply complementary, these theories are traditionally treated as conceptually separate, leaving implicit the mechanism by which probabilistic information can be reliably incorporated into deterministic computation. This paper introduces a high-level, non-operational framework that structurally unifies Shannon information theory and Turing computation through the concept of deterministic state representation. We formalize an axiomatic representational mapping that deterministically and reproducibly maps inputs into stable computational states, inducing equivalence classes and quotient-space semantics within which informational invariants and computational invariants can be jointly analyzed. Reproducibility and environmental invariance are treated as foundational axioms rather than implementation-dependent properties. The framework does not modify, subsume, or replace either Shannon’s or Turing’s theories, nor does it propose algorithms or system architectures. Instead, it clarifies a missing conceptual layer: the representational structure required for probabilistic information to support deterministic computation. By making this structure explicit, the paper provides a mathematically coherent lens through which information-theoretic and computation-theoretic descriptions can be understood within a single abstract model.

Keywords

Shannon information theory, Turing computation, deterministic representation, reproducible computation, information and computation, entropy, computability theory, deterministic state evolution, representation invariance, quotient space semantics, reproducibility, computational foundations, theoretical computer science, information theory foundations, deterministic computation law

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
Green