Related papers: On QBF Proofs and Preprocessing
A first-order conditional logic is considered, with semantics given by a variant of epsilon-semantics, where p -> q means that Pr(q | p) approaches 1 super-polynomially --faster than any inverse polynomial. This type of convergence is…
Entanglement is a crucial quantum resource with broad applications in quantum information science. For harnessing entanglement in practice, it is a prerequisite to certify the entanglement of a given quantum state. However, the…
Constructive analysis of feedback from clients often requires determining the cause of their sentiment from a substantial amount of text documents. To assist and improve the productivity of such endeavors, we leverage the task of…
Proof assistants are software-based tools that are used in the mechanization of proof construction and validation in mathematics and computer science, and also in certified program development. Different tools are being increasingly used in…
Quantum codes are subspaces of the state space of a quantum system that are used to protect quantum information. Some common classes of quantum codes are stabilizer (or additive) codes, non-stabilizer (or non-additive) codes obtained from…
Quantum coin flipping (QCF) is an essential primitive for quantum cryptography. Unconditionally secure strong QCF with an arbitrarily small bias was widely believed to be impossible. But basing on a problem which cannot be solved without…
This book is about conformal prediction and related inferential techniques that build on permutation tests and exchangeability. These techniques are useful in a diverse array of tasks, including hypothesis testing and providing uncertainty…
Quantum advantage is notoriously hard to find and even harder to prove. For example the class of functions computable with classical physics actually exactly coincides with the class computable quantum-mechanically. It is strongly believed,…
In recent years, many computational tasks have been proposed as candidates for showing a quantum computational advantage, that is an advantage in the time needed to perform the task using a quantum instead of a classical machine.…
Quantum Signal Processing (QSP) is a technique that can be used to implement a polynomial transformation $P(x)$ applied to the eigenvalues of a unitary $U$, essentially implementing the operation $P(U)$, provided that $P$ satisfies some…
Control Invariant (CI) sets are instrumental in certifying the safety of dynamical systems. Control Barrier Functions (CBFs) are effective tools to compute such sets, since the zero sublevel sets of CBFs are CI sets. However, computing CBFs…
A proof of quantumness is a type of challenge-response protocol in which a classical verifier can efficiently certify the quantum advantage of an untrusted prover. That is, a quantum prover can correctly answer the verifier's challenges and…
Incremental SAT and QBF solving potentially yields improvements when sequences of related formulas are solved. An incremental application is usually tailored towards some specific solver and decomposes a problem into incremental solver…
Control barrier functions (CBFs) are widely used in safety-critical controllers. However, constructing a valid CBF is challenging, especially under nonlinear or non-convex constraints and for high relative degree systems. Meanwhile, finding…
NLCertify is a software package for handling formal certification of nonlinear inequalities involving transcendental multivariate functions. The tool exploits sparse semialgebraic optimization techniques with approximation methods for…
Artificial intelligence assisted mathematical proof has become a highly focused area nowadays. One key problem in this field is to generate formal mathematical proofs from natural language proofs. Due to historical reasons, the formal proof…
Reasoning about quantum programs remains a fundamental challenge, regardless of the programming model or computational paradigm. Despite extensive research, existing verification techniques are insufficient -- even for quantum circuits, a…
Formally verifying system properties is one of the most effective ways of improving system quality, but its high manual effort requirements often render it prohibitively expensive. Tools that automate formal verification, by learning from…
Convex (specifically semidefinite) relaxation provides a powerful approach to constructing robust machine perception systems, enabling the recovery of certifiably globally optimal solutions of challenging estimation problems in many…
Control barrier function (CBF) has recently started to serve as a basis to develop approaches for enforcing safety requirements in control systems. However, constructing such function for a general system is a non-trivial task. This paper…