SAT Test Suite Package: Easy Tier Collection

 

🎯 Package Overview

Collection Name: Easy Tier Benchmark Suite

Total Instances: 10 SAT problems

Difficulty Range: Easy-A through Easy-B

Mixed Satisfiability: ✅ SAT + ❌ UNSAT instances

Package ID: easy-tier-v1.0

 

📊 Suite Composition

 

Hardness Distribution

 

Easy-A (1 instance): Trivial phase transition with minimal conflicts

Easy-B (9 instances): Small but structured problems with ultra-dense encoding

Satisfiability Distribution

SAT Instances (6): Satisfiable problems with ultra-dense symbolic encoding

UNSAT Instances (4): Unsatisfiable problems with efficient proof generation

Behavioral Categories

Ultra-Dense (9 instances): Extreme constraint density with symbolic/geometric encoding (26-43:1 ratios)

Phase-Transition (1 instance): Critical SAT/UNSAT boundary analysis (4.35:1 ratio)

Aggressive-Restarts (10 instances): Universal rapid restart strategies

Learning-Efficient (7 instances): Compact learned clauses with effective resolution

 

🔬 Technical Specifications

 

Structural Diversity

Variables: 60-282 (ultra-compact to medium-scale)

Clauses: 1,227-6,337 (wide clause count variation)

Clause-to-Variable Ratios: 4.35:1 - 43.43:1 (phase transition to revolutionary density)

Constraint Density: Standard (4:1) to Ultra-Dense (43:1)

 

Performance Characteristics

Conflict Range: 1 - 2,451 conflicts (easy tier scaling)

Solving Time Range: 0.15s - 0.24s (fast completion)

Efficiency Range: 7 - 11,200 conflicts/sec (ultra-wide efficiency variation)

Average Learned Clause Length: 4.28 - 33.5 (encoding-dependent)

 

🎪 Behavioral Fingerprints

 

Simplicity Patterns

Branching Strategies: Single VSID strategy (no complex switching needed)

Restart Policy: Geometric-stable (geom-stb) with minimal restart counts

Phase Transitions: Basic occur checking only

Distillation: None detected (problems too simple for advanced techniques)

 

Encoding-Specific Characteristics

Ultra-Dense Group: 26-43:1 ratios with symbolic/geometric encoding

Phase Transition Group: 4.35:1 ratio at critical boundary

Learned Clause Patterns: 4-33 length range based on encoding complexity

Restart Frequency: 1-13 restarts maximum (problems solve quickly)

 

🏆 Research Applications

 

Primary Use Cases

 

✅ Educational Foundation: Perfect introduction to SAT solving concepts

✅ Baseline Validation: Quick solver sanity checking and basic functionality

✅ Ultra-Dense Introduction: Entry-level exposure to extreme constraint density

✅ Algorithm Development: Fast iteration testing for new solver techniques

 

Benchmarking Advantages

Educational Progression: Natural stepping stone to moderate complexity

Quick Validation: Fast execution enables rapid testing cycles

Encoding Introduction: Safe introduction to ultra-dense symbolic patterns

Mixed Satisfiability: Both SAT and UNSAT examples at easy level

📈 Performance Expectations

 

Solver Efficiency Targets

 

Easy-A Instance: < 0.2 seconds (trivial completion) Easy-B Instances: 0.15-0.25 seconds (fast but varied by encoding)

Easy Tier Characteristics

Minimal Conflicts: 1-2,451 range with most under 1,500

Fast Resolution: All instances complete under 0.25 seconds

Simple Strategies: Single branching heuristic sufficient

Encoding Impact: Ultra-dense shows efficiency variation despite simplicity

 

🎓 Educational Value

 

Learning Focus

SAT Solving Basics: Introduction to fundamental concepts without complexity

Encoding Awareness: First exposure to different constraint encoding approaches

Performance Measurement: Understanding efficiency metrics in simple context

Mixed Satisfiability: Learning both SAT and UNSAT outcomes at basic level

 

Key Concepts Demonstrated

 

Basic SAT solving mechanics and terminology

Impact of constraint encoding on solver behavior

Efficiency measurement and interpretation

Satisfiability vs unsatisfiability recognition

 

 

File Type Breakdown

30 total files (3 files × 10 test instances)

10 .cnf files: DIMACS format SAT problem instances

10 .txt files: Raw solver execution logs with detailed traces

10 .md files: Processed behavioral analysis reports

1 README.md: Package documentation and usage guide

 

Recommended Usage

Educational Introduction: Start here before progressing to moderate complexity

Solver Validation: Quick functionality testing and sanity checking

Algorithm Development: Fast iteration testing for new techniques

Ultra-Dense Introduction: Safe first exposure to extreme constraint density

 

Compatibility

SAT Competition Format: Standard DIMACS CNF format, ready for any SAT solver

Solver Requirements: Basic SAT solver functionality sufficient

Resource Requirements: Minimal (60-282 variables, low memory footprint)