Project T : TestReducer - Algebraic Optimization of Engine Test Matrices Using Hecke Monoid Reduction

TestReducer is a software tool that applies algebraic properties from the Hecke monoid H₀(Ã₂) to optimize engine test matrices for automotive, aerospace, and marine applications. PROBLEMEngine dynamometer testing is expensive and time-consuming. A typical engine calibration involves 1,000-10,000 test points, with costs of €500-1,500 per hour. Analysis shows that 40-70% of test points in standard DoE (Design of Experiments) matrices are redundant, interpolable, or low-value. SOLUTIONTestReducer leverages two fundamental properties of the Hecke monoid:- Idempotence (a² = a): Same test conditions executed twice = single test- Braid relation (aba = bab): Some test sequences are equivalent regardless of order Combined with spatial interpolation analysis, these properties enable automatic identification of redundant tests. REDUCTION RULESThe tool implements six reduction rules:- TR001 - Idempotence: Detect duplicate test conditions (binned for tolerance)- TR002 - Interpolation: Mark interior points derivable from neighbors- TR003 - Transitivity: System tests predictable from component tests- TR004 - Equivalence: Detect equivalent test sequences- TR005 - Tolerance: Filter points within measurement uncertainty- TR006 - Prioritization: Rank by safety, certification, customer usage RESULTSIn benchmark testing with a 10×10 RPM/Load grid:- Input: 135 test points- Output: 38 test points- Reduction: 72%- Dyno time saved: 3.9 hours- Cost saved: €3,104 TECHNICAL DETAILS- Input formats: CSV (DoE matrices), JSON- Output formats: CSV, JSON, TXT reports- Dependencies: Python 3.8+ (standard library only)- License: MIT APPLICATIONS- Automotive engine development and calibration- Aerospace propulsion testing- Marine engine certification- HIL (Hardware-in-the-Loop) test optimization- Emissions certification campaigns This tool is part of Project T, exploring applications of algebraic idempotence properties to engineering verification domains including Infrastructure as Code, BIM clash detection, and engine testing.