Anders Franzén

The MathSAT 4 SMT Solver

We present MathSAT 4 , a state-of-the-art SMT solver. MathSAT 4 handles several useful theories: (combinations of) equality and uninterpreted functions, difference logic, linear arithmetic, and the theory of bit-vectors. It was explicitly designed for being used in formal verification, and thus provides functionalities which extend the applicability of SMT in this setting. In particular: model generation (for counterexample reconstruction), model enumeration (for predicate abstraction), an incremental interface (for BMC), and computation of unsatisfiable cores and Craig interpolants (for abstraction refinement).

Satisfiability modulo the theory of costs: foundations and applications

We extend the setting of Satisfiability Modulo Theories (SMT) by introducing a theory of costs

Delayed theory combination vs. Nelson-Oppen for satisfiability modulo theories: a comparative analysis

{\mathcal{C}}

Using Satisfiability Modulo Theories for Inductive Verification of Lustre Programs

, where it is possible to model and reason about resource consumption and multiple cost functions, e.g., battery, time, and space. We define a decision procedure that has all the features required for the integration withint the lazy SMT schema: incrementality, backtrackability, construction of conflict sets, and deduction. This naturally results in an SMT solver for the disjoint union of

Optimizing monitoring requirements in self-adaptive systems

{\mathcal{C}}

Tighter integration of BDDs and SMT for predicate abstraction

and any other theory

A lazy and layered SMT(BV) solver for hard industrial verification problems

{\mathcal{T}}

Encoding RTL Constructs for MathSAT: a Preliminary Report

. This framework has two important applications. First, we tackle the problem of Optimization Modulo Theories: rather than checking the existence of a satisfying assignment, as in SMT, we require a satisfying assignment that minimizes a given cost function. We build on the decision problem for SMT with costs, i.e., finding a satisfying assigniment with cost within an admissibility range, and propose two algorithms for optimization. Second, we use multiple cost functions to deal with PseudoBoolean constraints. Within the

Delayed theory combination vs. nelson-oppen for satisfiability modulo theories: a comparative analysis

{\text{SMT}({\mathcal C})}

Applying SMT in symbolic execution of microcode

framework, the effectively PseudoBoolean constraints are dealt with by the cost solver, while the other constraints are reduced to pure boolean reasoning. We implemented the proposed approach within the MathSAT SMT solver, and we experimentally evaluated it on a large set of benchmarks, also from industrial applications. The results clearly demonstrate the potential of the approach.