PulseExploreJournal ClubDebatesTrendingResearchersJournals
Instagram
HomeExploreJournal ClubTrending
Synapse
⌘+K
Synapse
February 6, 20260 citationsOpen Access

On the Structural Impossibility of Local Constructions for Global Semantic Irreducibility

View Full Paper
MAMichael Arias

Key Points

  • The paper aims to explore the relationship between local constraints and global irreducibility in computational problems.
  • Introduces the Global Semantic Entanglement Index to measure irreducibility.
  • Analyzes various local constructions theoretically and through experiments.
  • Develops a meta-theorem linking local properties to global outcomes.
  • Broad classes of constructs, including EXACTLY-ONE gadgets, collapse to constant entanglement.
  • Demonstrates that local reversibility and semantic monotonicity obstruct global irreducibility.
  • Delimits the search space for possible P versus NP separations.

Abstract

This paper investigates whether globally irreducible dependencies, which are necessary for separating P from NP under structural frameworks based on computational invariance, can arise from locally specified constraint systems. Building on earlier work that reduced P versus NP to the existence of DGNL, it introduces the Global Semantic Entanglement Index as a quantitative measure of irreducibility. Through theoretical analysis and systematic experimentation, it shows that broad classes of constructions—including EXACTLY-ONE gadgets, Tseitin systems, and monotone irreversible constraints—collapse to constant entanglement. A meta-theorem proves that local reversibility and semantic monotonicity prevent global irreducibility. The results sharply delimit the remaining search space for P versus NP separations.

Ask AI
Helpful
Bookmark
Share
View Full Paper

Cite This Study

Michael Arias (2026) studied this question.

synapsesocial.com/papers/698585ea8f7c464f23009bcfhttps://doi.org/10.5281/zenodo.18483179
Ask AI
Helpful
Bookmark
Share
View Full Paper

Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

  1. 1Global Irreducible Dependencies, Local Indistinguishability, and a Structural Reduction of the P vs. NP Problem2026
  2. 2Global Dependence, Reductions, and Semantic Fragmentation in NP-Complete Problems2026
  3. 3Irreducible Global Dependencies, Structural Exposure, and a Conditional Separation Framework for P versus NP2026
  4. 4Confluent Semantics, Local Certification, and a Structural Reformulation of the P versus NP Problem2026
  5. 5Irreducible Global Dependencies, Informational Monotonicity, and a Structural Obstruction to Deterministic Polynomial-Time Computation2026