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| Format: | Recurso digital |
| Language: | English |
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2025
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| Online Access: | https://doi.org/10.5281/zenodo.17354014 |
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| author | CARRASCO RAMIREZ, JOSE GABRIEL |
| author_facet | CARRASCO RAMIREZ, JOSE GABRIEL |
| contents | <p><strong>From Physics as Computation to State-Parallel Computing</strong> develops the theoretical and semantic foundations of the State-Parallel Computing (SPC) paradigm, building upon the conceptual framework introduced in "State-Parallel Computing: Physical Governance as the Third Paradigm."</p> <p>This work formalizes computation as <strong>governed physical evolution</strong> on a state manifold Φ, constrained by a feasibility mask M, and evolved by a governed semigroup {Λₜ}. Within this framework, <strong>correctness becomes a property of physical invariance</strong> rather than post-execution verification.</p> <p>The paper defines both <strong>denotational and operational semantics</strong> for SPC. Denotationally, meaning corresponds to feasible ω-limit sets; operationally, execution unfolds through the <strong>Compilation–Iteration–Projection–Recovery (CIPR) cycle</strong>, linking compilation choices to runtime physics. Key results include the <strong>No-Bypass invariance theorem</strong>, Lyapunov-based correctness, exponential convergence rates, and ISS-type robustness under tangent perturbations.</p> <p>By unifying <strong>viability theory, projection dynamics, and Lyapunov stability</strong>, SPC establishes a mathematical contract between semantics and physical law—providing the rigorous basis for compiler and runtime design in hybrid physical substrates.</p> <p><strong>Relationship to Series:</strong> This paper serves as the <strong>semantic foundation</strong> for the SPC framework introduced in the first installment, completing the theoretical arc from paradigm definition to formal semantics.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17354014 |
| institution | Zenodo |
| language | eng |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | From Physics as Computation to State-Parallel Computing: Theoretical Foundations and Unified Semantics CARRASCO RAMIREZ, JOSE GABRIEL State-Parallel Computing, Physical Computation, Formal Semantics, Governed Attraction, Feasibility Masks, Viability Theory, Projected Dynamics, CIPR Cycle, Computational Physics, Dynamical Systems Semantics Computer Systems computer science Theoretical computer science Computational physics Dynamical systems Dynamical systems Emerging Technologies <p><strong>From Physics as Computation to State-Parallel Computing</strong> develops the theoretical and semantic foundations of the State-Parallel Computing (SPC) paradigm, building upon the conceptual framework introduced in "State-Parallel Computing: Physical Governance as the Third Paradigm."</p> <p>This work formalizes computation as <strong>governed physical evolution</strong> on a state manifold Φ, constrained by a feasibility mask M, and evolved by a governed semigroup {Λₜ}. Within this framework, <strong>correctness becomes a property of physical invariance</strong> rather than post-execution verification.</p> <p>The paper defines both <strong>denotational and operational semantics</strong> for SPC. Denotationally, meaning corresponds to feasible ω-limit sets; operationally, execution unfolds through the <strong>Compilation–Iteration–Projection–Recovery (CIPR) cycle</strong>, linking compilation choices to runtime physics. Key results include the <strong>No-Bypass invariance theorem</strong>, Lyapunov-based correctness, exponential convergence rates, and ISS-type robustness under tangent perturbations.</p> <p>By unifying <strong>viability theory, projection dynamics, and Lyapunov stability</strong>, SPC establishes a mathematical contract between semantics and physical law—providing the rigorous basis for compiler and runtime design in hybrid physical substrates.</p> <p><strong>Relationship to Series:</strong> This paper serves as the <strong>semantic foundation</strong> for the SPC framework introduced in the first installment, completing the theoretical arc from paradigm definition to formal semantics.</p> |
| title | From Physics as Computation to State-Parallel Computing: Theoretical Foundations and Unified Semantics |
| topic | State-Parallel Computing, Physical Computation, Formal Semantics, Governed Attraction, Feasibility Masks, Viability Theory, Projected Dynamics, CIPR Cycle, Computational Physics, Dynamical Systems Semantics Computer Systems computer science Theoretical computer science Computational physics Dynamical systems Dynamical systems Emerging Technologies |
| url | https://doi.org/10.5281/zenodo.17354014 |