Finite model finding in satisfiability modulo theories

Counterexample-Guided Quantifier Instantiation for Synthesis in SMT

“…A simple way to limit the size of the candidate solutions is to consider smaller programs before larger ones. Adapting techniques for finding finite models of minimal size [25], we use a strategy that starting, from n = 0, searches for programs of size n + 1 only after its has exhausted the search for programs of size n. In solvers based on the DPLL(T ) architecture, like CVC4, this can be accomplished by introducing a splitting lemma of the form (size(e) ≤ 0 ∨ ¬size(e) ≤ 0) and asserting size(e) ≤ 0 as the first decision literal, where size is a function symbol of type σ → Int for every datatype sort σ and stands for the function that maps each datatype value to its term size (i.e., the number of non-nullary constructor applications in the term). We do the same for size(e) ≤ 1 if and when ¬size(e) ≤ 0 becomes asserted.…”

Constraint solving for finite model finding in SMT solvers

“…Section 9 describes an experimental evaluation of our implementation of these techniques in the SMT solver cvc4 on several sets of benchmarks. This paper builds on material from previous conference papers [29,30], as well as the PhD dissertation by the first author [32].…”

Automated reasoning over string constraints

“…Bounded integer quantification is a special extension of the fair strategy. It is refutation sound and model complete [76]. Since the modeling procedure is precise without any approximation, these string functions are also refutation sound and model complete, i.e., if the constraints are satisfiable, the produce can find a model if fairness is applied.…”

“…Since this thesis does not focus on how to solve quantified formulas, we use a fairly simple rule Q-Inst in Figure 3.18 to mimic the approach for handling quantified formulas. The actual approach is more sophisticated and discussed in [76].…”

“…One idea is to solve negative membership constraints without applying the complementation operation. We adopt the idea of finite model finding in solving quantified formulas [76]. We reduce negative membership constraints to quantified formulas over bounded integers.…”