A survey of symbolic execution techniques

R Baldoni, E Coppa, DC D'elia, C Demetrescu… - ACM Computing …, 2018 - dl.acm.org
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 …

[HTML][HTML] Deciding the consistency of non-linear real arithmetic constraints with a conflict driven search using cylindrical algebraic coverings

E Ábrahám, JH Davenport, M England… - Journal of Logical and …, 2021 - Elsevier
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 …

[HTML][HTML] Cylindrical algebraic decomposition with equational constraints

M England, R Bradford, JH Davenport - Journal of Symbolic Computation, 2020 - Elsevier
Abstract Cylindrical Algebraic Decomposition (CAD) has long been one of the most
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

C Bright, I Kotsireas, V Ganesh - Journal of Symbolic Computation, 2020 - Elsevier
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 …

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 …

Comparing machine learning models to choose the variable ordering for cylindrical algebraic decomposition

M England, D Florescu - … , CICM 2019, Prague, Czech Republic, July 8–12 …, 2019 - Springer
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 …

The DEWCAD project: pushing back the doubly exponential wall of cylindrical algebraic decomposition

R Bradford, JH Davenport, M England… - … in Computer Algebra, 2022 - dl.acm.org
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 …

Using machine learning to improve cylindrical algebraic decomposition

Z Huang, M England, DJ Wilson, J Bridge… - … in Computer Science, 2019 - Springer
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 …

Algorithmically generating new algebraic features of polynomial systems for machine learning

D Florescu, M England - arxiv preprint arxiv:1906.01455, 2019 - arxiv.org
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 …

New opportunities for the formal proof of computational real geometry?

J Davenport, M England, G Kremer, Z Tonks - arxiv preprint arxiv …, 2020 - arxiv.org
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 …