Ulrich Loup

SMT-RAT: an SMT-compliant nonlinear real arithmetic toolbox

We present

On Gröbner Bases in the Context of Satisfiability-Modulo-Theories Solving over the Real Numbers

\texttt{SMT-RAT}

GiNaCRA: a C++ library for real algebraic computations

, a

On collaboratively conveying computer science to pupils

\texttt{C++}

I-RiSC: an SMT-compliant solver for the existential fragment of real algebra

toolbox offering theory solver modules for the development of SMT solvers for nonlinear real arithmetic (NRA). NRA is an important but hard-to-solve theory and only fragments of it can be handled by some of the currently available SMT solvers. Our toolbox contains modules implementing the virtual substitution method, the cylindrical algebraic decomposition method, a Grobner bases simplifier and a general simplifier. These modules can be combined according to a user-defined strategy in order to exploit their advantages.

A symbiosis of interval constraint propagation and cylindrical algebraic decomposition

We address satisfiability checking for the first-order theory of the real-closed field (RCF) using satisfiability-modulo-theories (SMT) solving. SMT solvers combine a SAT solver to resolve the Boolean structure of a given formula with theory solvers to verify the consistency of sets of theory constraints.

A Lazy SMT-Solver for a Non-Linear Subset of Real Algebra

We present the growing C++ library GiNaCRA, which provides efficient and easy-to-integrate data structures and methods for real algebra. It is based on the C++ library GiNaC, supporting the symbolic representation and manipulation of polynomials. In contrast to other similar tools, our open source library aids exact, real algebraic computations based on an appropriate data type representing real zeros of polynomials. The only non-standard library GiNaCRA depends on is GiNaC, which makes the installation and usage of our library simple. Our longterm goal is to integrate decision procedures for real algebra within the Satisfiability-Modulo-Theories (SMT) context and thereby provide tool support for many applied formal methods.

SMT-RAT: An SMT-Compliant Nonlinear Real Arithmetic Toolbox - (Tool Presentation).

Though there is an increasing need for computer scientists in our society, gifted young people with strong mathematical background, who would be well-suited for a study of computer science, often do not consider this choice because they have a wrong picture of computer science in mind. In this paper we present a new concept of collaborative learning to introduce high-school students to the field of theoretical computer science. In particular, we choose the demanding field of real-time systems in order to illustrate the applicability of theoretical methods on real-world systems. Statistical results show that with our concept we are able to point out the manifoldness, beauty and challenge of this scientific area and can convince high-school students to consider computer science as a choice of study.

SMT-Solving for the First-Order Theory of the Reals

This paper connects research in computer science in the field of SAT-modulo-theories (SMT) solving and research in mathematics on decision procedures for real algebra. We consider a real algebraic decision procedure computing all realizable sign conditions of a set of polynomials. We modify this procedure so that it satisfies certain requirements needed for the embedding into an SMT-solver.