Lemmas on Demand for Satisfiability Solvers

Lambdas, Arrays and Quantifiers

Satisfiability Modulo Theories (SMT) refers to the problem of deciding the satisfiability of a first-order formula with respect to one or more first-order theories. In many applications of hardware and software verification, SMT solvers are employed as back-end engine to solve complex verification tasks that usually combine multiple theories, such as the theory of fixed-size bit-vectors and the...

Lemmas on Demand for Satis ability Solvers

Satisfiability Solvers

Satisfiability (SAT) solvers have become powerful tools to solve a wide range of applications. In case SAT problems are satisfiable, it is easy to validate a witness. However, if SAT problems have no solutions, a proof of unsatisfiability is required to validate that result. Apart from validation, proofs of unsatisfiability are useful in several applications, such as interpolation [50] and extr...

Parallel Resolution of the Satisfiability Problem: A Survey

The past few years have seen enormous progress in the performance of propositional satisfiability (SAT) solvers, and consequently SAT solvers are widely used in industry for many applications. In spite of this progress, there is strong demand for higher SAT algorithms efficiency to solve harder and larger problems. Unfortunately, most modern solvers are sequential and fewer are parallel. Our in...

Lemmas on Demand for Lambdas

We generalize the lemmas on demand decision procedure for array logic as implemented in Boolector to handle non-recursive and non-extensional lambda terms. We focus on the implementation aspects of our new approach and discuss the involved algorithms and optimizations in more detail. Further, we show how arrays, array operations and SMT-LIB v2 macros are represented as lambda terms and lazily h...