Automated Reasoning: satisfiability

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  • SAT/SMT basics, SAT examples
    • This module introduces SAT (satisfiability) and SMT (SAT modulo theories) from scratch, and gives a number of examples of how to apply SAT.
  • SMT applications
    • This module shows a number of applications of satisfiability modulo the theory of linear inequalities (SMT)
  • Theory and algorithms for CNF-based SAT
    • This module describes how a rule called Resolution serves to determine whether a propositional formula in conjunctive normal form (CNF) is unsatisfiable. It is shown how an approach called DPLL does the same job, and how it is related to resolution. Finally, it is shown how current SAT solvers essentially implement and optimize DPLL.
  • Theory and algorithms for SAT/SMT
    • This module consists of two parts.
      The first part is about transforming arbitrary propositional formulas to CNF, leading to the Tseitin transformation doing this job such that the size of the transformed formula is linear in the size of the original formula.
      The second part is about extending SAT to SMT, in particular to dealing with linear inequalities. It is shown how the Simplex method for linear optimization serves for this job; the Simplex method itself is explained in detail.