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This chapter introduces the approach of satisfiability modulo theory (SMT) as DPLL(T), which extends the DPLL algorithm by incorporating theory T. To support DPLL(T), it describes several mature algorithms for equality with uninterpreted functions, linear arithmetic, integer programming, and the difference logic. Then Nelson and Oppen’s algorithm is presented, which can combine multiple theories. The chapter ends with an introduction to SMT-LIB (a library of SMT problems) and SMT-COMP (competition of SMT solvers).

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Decision Procedures

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  • 发表日期：

    2025年

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  • Hantao Zhang,
  • Jian Zhang

摘要

This chapter introduces the approach of satisfiability modulo theory (SMT) as DPLL(T), which extends the DPLL algorithm by incorporating theory T. To support DPLL(T), it describes several mature algorithms for equality with uninterpreted functions, linear arithmetic, integer programming, and the difference logic. Then Nelson and Oppen’s algorithm is presented, which can combine multiple theories. The chapter ends with an introduction to SMT-LIB (a library of SMT problems) and SMT-COMP (competition of SMT solvers).