Treffer: Structural Barriers as Communication Bottlenecks: A Novel Perspective on SAT Algorithmic Limitations

This groundbreaking research establishes the first formal connection between **structural barriers in SAT solving** and **communication complexity theory**. By interpreting structurally-constrained (S_C) algorithms as communication channels with limited bandwidth, we prove fundamental lower bounds on their effectiveness and demonstrate exponential gaps between structural and semantic approaches. Theoretical Breakthroughs: - **Communication complexity framework** for analyzing S_C-algorithm limitations - **Exponential separations** using Circuit Value Problem constructions - **Information loss bounds** L_σ(n) = Ω(n³) for canonical representations - **First structural-specific lower bounds** for SAT algorithms Practical Applications: - **Structural Complexity Barometer** for instance difficulty assessment - **Desymmetrization preprocessors** for breaking false symmetry patterns - **Integration guidelines** for hybrid structural-semantic solvers - **Performance prediction tools** for industrial SAT solving Methodological Innovation - **AI-assisted theoretical discovery** through human-Gemini collaboration - **Deterministic constructions** of overlap gap property instances - **Open-source framework** for continued research and applications. Research Significance: This work represents a **paradigm-shifting contribution** to theoretical computer science by: 1. **Proving fundamental limitations** - The observed 75% accuracy gap is confirmed as a fundamental limitation, not an algorithmic deficiency 2. **Opening new research directions** - Creates the field of structural barrier analysis in computational complexity 3. **Bridging theory and practice** - Provides immediate applications for industrial SAT solving while advancing theoretical understanding 4. **Demonstrating AI-human collaboration** - Shows how AI insights can guide breakthrough theoretical research Comprehensive Testing: - **256 controlled experiments** across diverse SAT instance families - **Statistical significance** p < 0.001 with effect size Cohen's ...