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Explore a groundbreaking algorithm for eliminating Ramsey quantifiers from Linear Integer Arithmetic (LIA), Linear Real Arithmetic (LRA), and Linear Integer Real Arithmetic (LIRA) in this 19-minute conference talk from POPL 2024. Delve into the applications of Satisfiability Modulo Theories (SMT) enriched with Ramsey quantifiers in proving program termination and monadic decomposability of SMT formulas. Learn how this new approach enables efficient handling of well-foundedness checks by SMT-solvers and provides a uniform semi-algorithm for verifying termination and liveness in various infinite-state systems. Discover the solution to an open problem on checking monadic decomposability in quantifier-free fragments of LRA and LIRA, with implications for automated reasoning and constraint databases. Gain insights into the experimental results of a prototype implementation on micro-benchmarks, demonstrating the practical potential of this innovative technique.
