A survey of symbolic execution techniques
Many security and software testing applications require checking whether certain properties
of a program hold for any possible usage scenario. For instance, a tool for identifying …
of a program hold for any possible usage scenario. For instance, a tool for identifying …
[HTML][HTML] Deciding the consistency of non-linear real arithmetic constraints with a conflict driven search using cylindrical algebraic coverings
We present a new algorithm for determining the satisfiability of conjunctions of non-linear
polynomial constraints over the reals, which can be used as a theory solver for satisfiability …
polynomial constraints over the reals, which can be used as a theory solver for satisfiability …
[HTML][HTML] Cylindrical algebraic decomposition with equational constraints
Abstract Cylindrical Algebraic Decomposition (CAD) has long been one of the most
important algorithms within Symbolic Computation, as a tool to perform quantifier elimination …
important algorithms within Symbolic Computation, as a tool to perform quantifier elimination …
[HTML][HTML] Applying computer algebra systems with SAT solvers to the Williamson conjecture
We employ tools from the fields of symbolic computation and satisfiability checking—namely,
computer algebra systems and SAT solvers—to study the Williamson conjecture from …
computer algebra systems and SAT solvers—to study the Williamson conjecture from …
Thirty years of virtual substitution: Foundations, techniques, applications
T Sturm - Proceedings of the 2018 ACM International …, 2018 - dl.acm.org
In 1988, Weispfenning published a seminal paper introducing a substitution technique for
quantifier elimination in the linear theories of ordered and valued fields. The original focus …
quantifier elimination in the linear theories of ordered and valued fields. The original focus …
Comparing machine learning models to choose the variable ordering for cylindrical algebraic decomposition
There has been recent interest in the use of machine learning (ML) approaches within
mathematical software to make choices that impact on the computing performance without …
mathematical software to make choices that impact on the computing performance without …
The DEWCAD project: pushing back the doubly exponential wall of cylindrical algebraic decomposition
This abstract seeks to introduce the ISSAC community to the DEWCAD project, which is
based at Coventry University and the University of Bath, in the United Kingdom. The project …
based at Coventry University and the University of Bath, in the United Kingdom. The project …
Using machine learning to improve cylindrical algebraic decomposition
Abstract Cylindrical Algebraic Decomposition (CAD) is a key tool in computational algebraic
geometry, best known as a procedure to enable Quantifier Elimination over real-closed …
geometry, best known as a procedure to enable Quantifier Elimination over real-closed …
Algorithmically generating new algebraic features of polynomial systems for machine learning
There are a variety of choices to be made in both computer algebra systems (CASs) and
satisfiability modulo theory (SMT) solvers which can impact performance without affecting …
satisfiability modulo theory (SMT) solvers which can impact performance without affecting …
New opportunities for the formal proof of computational real geometry?
The purpose of this paper is to explore the question" to what extent could we produce formal,
machine-verifiable, proofs in real algebraic geometry?" The question has been asked before …
machine-verifiable, proofs in real algebraic geometry?" The question has been asked before …