Related papers: On Symmetry and Quantification: A New Approach to …
We show that the requirement of manifest coordinate invariance of perturbatively defined quantum-mechanical path integrals in curved space leads to an extension of the theory of distributions by specifying unique rules for integrating…
We address the problem of uncertainty quantification for the deconvolution model \(Z = X + Y\), where \(X\) and \(Y\) are nonnegative random variables and the goal is to estimate the signal's distribution of \(X \sim F_0\) supported…
The continuous-variable quantum key distribution with entanglement in the middle, a semi-device-independent protocol, places the source at the untrusted third party between Alice and Bob, and thus has the advantage of high levels of…
We consider the problem of coordinating a collection of switched subsystems under both local and global constraints for safe operation of the system. Although an invariant set can be leveraged to construct a safety-guaranteed controller for…
The Intrinsic Dimension (ID) is a key concept in unsupervised learning and feature selection, as it is a lower bound to the number of variables which are necessary to describe a system. However, in almost any real-world dataset the ID…
First-order logic, and quantifiers in particular, are widely used in deductive verification. Quantifiers are essential for describing systems with unbounded domains, but prove difficult for automated solvers. Significant effort has been…
Automatic verification of concurrent programs faces state explosion due to the exponential possible interleavings of its sequential components coupled with large or infinite state spaces. An alternative is deductive verification, where…
The automatic verification of programs that maintain unbounded low-level data structures is a critical and open problem. Analyzers and verifiers developed in previous work can synthesize invariants that only describe data structures of…
We introduce a general methodology for quantitative model checking and control synthesis with supermartingale certificates. We show that every specification that is invariant to time shifts admits a stochastic invariant that bounds its…
In a recent paper, the authors proposed a general methodology for probabilistic learning on manifolds. The method was used to generate numerical samples that are statistically consistent with an existing dataset construed as a realization…
We explore the power of interactive proofs with a distributed verifier. In this setting, the verifier consists of $n$ nodes and a graph $G$ that defines their communication pattern. The prover is a single entity that communicates with all…
We consider the problem of solving a distributed optimization problem using a distributed computing platform, where the communication in the network is limited: each node can only communicate with its neighbours and the channel has a…
Two characteristics that make convex decomposition algorithms attractive are simplicity of operations and generation of parallelizable structures. In principle, these schemes require that all coordinates update at the same time, i.e., they…
State preparation is a cornerstone of quantum technologies, underpinning applications in computation, communication, and sensing. Its importance becomes even more pronounced in non-Markovian open quantum systems, where environmental memory…
We study parity features as representations that can be evaluated entirely classically once the binary or quantized input representation and parity words are fixed, particularly when labels depend on higher-order feature interactions or…
This paper addresses the complexity of SAT-based invariant inference, a prominent approach to safety verification. We consider the problem of inferring an inductive invariant of polynomial length given a transition system and a safety…
A fundamental challenge in multiparameter persistent homology is the absence of a complete and discrete invariant. To address this issue, we propose an enhanced framework that realizes a holistic understanding of a fully commutative…
Incremental determinization is a recently proposed algorithm for solving quantified Boolean formulas with one quantifier alternation. In this paper, we formalize incremental determinization as a set of inference rules to help understand the…
We revisit the classic problem of proving safety over parameterised concurrent systems, i.e., an infinite family of finite-state concurrent systems that are represented by some finite (symbolic) means. An example of such an infinite family…
The compressive learning framework reduces the computational cost of training on large-scale datasets. In a sketching phase, the data is first compressed to a lightweight sketch vector, obtained by mapping the data samples through a…