Related papers: A First Complete Algorithm for Real Quantifier Eli…
We present two new algorithms for the computation of the q-integer linear decomposition of a multivariate polynomial. Such a decomposition is essential for the treatment of q-hypergeometric symbolic summation via creative telescoping and…
First-order model counting emerged recently as a novel reasoning task, at the core of efficient algorithms for probabilistic logics. We present a Skolemization algorithm for model counting problems that eliminates existential quantifiers…
This extended abstract accompanies an invited talk at CASC 2024, which surveys recent developments in Real Quantifier Elimination (QE) and Cylindrical Algebraic Decomposition (CAD). After introducing these concepts we will first consider…
We consider a modification of the Quantifier Elimination (QE) problem called Partial QE (PQE). In PQE, only a small part of the formula is taken out of the scope of quantifiers. The appeal of PQE is that many verification problems, e.g.…
We describe SeCaV, a sequent calculus verifier for first-order logic in Isabelle/HOL, and the SeCaV Unshortener, an online tool that expands succinct derivations into the full SeCaV syntax. We leverage the power of Isabelle/HOL as a proof…
The need for formal definition of the very basis of mathematics arose in the last century. The scale and complexity of mathematics, along with discovered paradoxes, revealed the danger of accumulating errors across theories. Although,…
The "quantum duality principle" states that a quantisation of a Lie bialgebra provides also a quantisation of the dual formal Poisson group and, conversely, a quantisation of a formal Poisson group yields a quantisation of the dual Lie…
On the one hand, ordered completion is a fundamental technique in equational theorem proving that is employed by automated tools. On the other hand, their complexity makes such tools inherently error prone. As a remedy to this situation we…
We present a formalization of basics related to infinite words in the generic proof assistant Isabelle/HOL. Furthermore, we present a formalization of purely morphic and morphic languages. Finally, we present a formalized definition of…
This paper builds and extends on the authors' previous work related to the algorithmic tool, Cylindrical Algebraic Decomposition (CAD), and one of its core applications, Real Quantifier Elimination (QE). These topics are at the heart of…
We present a proof procedure for univariate real polynomial problems in Isabelle/HOL. The core mathematics of our procedure is based on univariate cylindrical algebraic decomposition. We follow the approach of untrusted certificates,…
Quantifier-elimination or model-completeness of the affine part of some classical first order theories are proved.
The formalisation of mathematics is continuing rapidly, however combinatorics continues to present challenges to formalisation efforts, such as its reliance on techniques from a wide range of other fields in mathematics. This paper presents…
Modern machine learning pipelines are built on numerical algorithms. Reliable numerical methods are thus a prerequisite for trustworthy machine learning and cyber-physical systems. Therefore, we contribute a framework for verified numerical…
We develop a quantum-classical hybrid algorithm to calculate the analytical second-order derivative of the energy for the orbital-optimized variational quantum eigensolver (OO-VQE), which is a method to calculate eigenenergies of a given…
Quantum information has the property that measurement is an inherently destructive process. This feature is most apparent in the principle of complementarity, which states that mutually incompatible observables cannot be measured at the…
The Learning-With-Errors (LWE) problem is a fundamental computational challenge with implications for post-quantum cryptography and computational learning theory. Here we propose a quantum-classical hybrid algorithm with Ising model to…
The paper presents our research on quantifier elimination (QE) for compositional reasoning and verification. For compositional reasoning, QE provides the foundation of our approach, serving as the calculus for composition to derive the…
We extend a semantic verification framework for hybrid systems with the Isabelle/HOL proof assistant by an algebraic model for hybrid program stores, a shallow expression model for hybrid programs and their correctness specifications, and…
This paper presents two enhancements to cylindrical algebraic decomposition (CAD) based quantifier elimination (QE) for cases in which multiple equational constraints are present in the given input formula $\phi^*$. The first enhancement…