Functional constraints capture Boolean relationships among signal nets by analyzing the functionality of a circuit. Such constraints find widespread application in VLSI design methodology and can be derived using various techniques. The size and complexity of these constraints becomes a limiting factor in their successful usage for large designs. This paper describes CONAN (Constraint Analyzer), a powerful framework to analyze and simplify such constraints. CONAN is built on the solution to a novel minimization problem. The feasibility and effectiveness of CONAN is demonstrated by using it for functional untestability analysis of large industrial benchmarks. Run-times were reduced from over a week to less than 30 minutes. Additionally, unique functionally untestable faults were derived using this approach when compared with constraints provided by designers.