SAT and SMT: Their Algorithm Designs and Applications

Abstract

SAT and SMT (SAT modulo theory) solvers aim to find a satisfiable instance of given constraints. SAT solver accepts a boolean constraints in a conjunctive normal form (CNF), such as, and if a CNF is satisfiable, returns an instance, such as. SMT solver accepts constraints described in background theory, such as arithmetic. Part 1 is devoted to explain the textbook concepts and usage of SAT and SMT solvers. For their usage, we investigate how to encode problems into CNF. Examples are taken from puzzles. Although puzzles are problems on bounded domains, there is certain hierarchy of difficulties, corresponding to the logical hierarchy of problems. Our examples are SUDOKU [2], Logic pictures [3], and Slither link [4] 1, 2, which correspond to descriptions in CNF, general propositional logic, and higher order logic, respectively. As conversion techniques to efficient CNFs, a popular Tseitin conversion and two special techniques (for the latter two, respectively) are introduced. If time allows, we will overview on de-facto-standard algorithm designs for SAT solvers, i.e., non-chronological back tracking with implication graphs, conflict driven learning and reset, and two watched literals [1].