A Uniqueness Theorem for Distributed Computation under Physical Constraint

2025-09-15

AI Summary

In extreme environments—such as in-network computing—achieving high communication efficiency, low memory footprint, and scalability simultaneously remains a fundamental tri-lemma. Method: This paper shifts from engineering trade-offs to a physics-constraint-driven design paradigm, introducing the first axiomatized system grounded in hardware laws. It formally proves that, among idempotent-mergeable operation classes, Self-Describing Parallel Flows (SDPF) constitute the unique optimal distributed computing paradigm. Leveraging formal methods, the work unifies distributed systems theory with dataflow models, yielding stateless executors and control-logic-embedded dataflow mechanisms. Contribution/Results: We establish that SDPF guarantees convergence, Turing completeness, and minimality—providing the first physically grounded, provably necessary foundation for distributed architectures under stringent physical constraints.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Distributed Search
• Data Mining & Knowledge Management: Scalability, Parallel & Distributed Systems

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Federated Web and WoT systems, including distributed, federated and edge-based data processing
• Security and Privacy: Data transparency and provenance
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

Foundational models of computation often abstract away physical hardware limitations. However, in extreme environments like In-Network Computing (INC), these limitations become inviolable laws, creating an acute trilemma among communication efficiency, bounded memory, and robust scalability. Prevailing distributed paradigms, while powerful in their intended domains, were not designed for this stringent regime and thus face fundamental challenges. This paper demonstrates that resolving this trilemma requires a shift in perspective - from seeking engineering trade-offs to deriving solutions from logical necessity. We establish a rigorous axiomatic system that formalizes these physical constraints and prove that for the broad class of computations admitting an idempotent merge operator, there exists a unique, optimal paradigm. Any system satisfying these axioms must converge to a single normal form: Self-Describing Parallel Flows (SDPF), a purely data-centric model where stateless executors process flows that carry their own control logic. We further prove this unique paradigm is convergent, Turing-complete, and minimal. In the same way that the CAP theorem established a boundary for what is impossible in distributed state management, our work provides a constructive dual: a uniqueness theorem that reveals what is extit{inevitable} for distributed computation flows under physical law.

Problem

• Resolving trilemma among communication efficiency, bounded memory, scalability
• Deriving optimal distributed computation paradigm from physical constraints
• Establishing uniqueness theorem for inevitable computation flows under physical law

Innovation

• Axiomatic system formalizing physical constraints
• Unique optimal paradigm for idempotent computations
• Self-Describing Parallel Flows data-centric model