Related papers: Pseudo-deterministic Proofs
As humans come to rely on autonomous systems more, ensuring the transparency of such systems is important to their continued adoption. Explainable Artificial Intelligence (XAI) aims to reduce confusion and foster trust in systems by…
A recent line of work initiated by Chiesa and Gur and further developed by Herman and Rothblum investigates the sample and communication complexity of verifying properties of distributions with the assistance of a powerful, knowledgeable,…
Symbolic Execution is a formal method that can be used to verify the behavior of computer programs and detect software vulnerabilities. Compared to other testing methods such as fuzzing, Symbolic Execution has the advantage of providing…
Achieving quantum computational advantage requires solving a classically intractable problem on a quantum device. Natural proposals rely upon the intrinsic hardness of classically simulating quantum mechanics; however, verifying the output…
In this brief semi-expository article we present a few efficient techniques for calculating and proving determinantal identities. Several stimulating examples of different flavor and applications are spread across the pages which we hope…
Past research on probabilistic databases has studied the problem of answering queries on a static database. Application scenarios of probabilistic databases however often involve the conditioning of a database using additional information…
Runtime efficiency and termination are crucial properties in the studies of program verification. Instead of dealing with these issues in an ad hoc manner, it would be useful to develop a robust framework in which such properties are…
Mechanical reasoning is a key area of research that lies at the crossroads of mathematical logic and artificial intelligence. The main aim to develop mechanical reasoning systems (also known as theorem provers) was to enable mathematicians…
The lower and upper bound of any given algorithm is one of the most crucial pieces of information needed when evaluating the computational effectiveness for said algorithm. Here a novel method of Boolean Algebraic Programming for symbolic…
We study planning problems where autonomous agents operate inside environments that are subject to uncertainties and not fully observable. Partially observable Markov decision processes (POMDPs) are a natural formal model to capture such…
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…
Many real-world sequential decision-making problems involve critical systems with financial risks and human-life risks. While several works in the past have proposed methods that are safe for deployment, they assume that the underlying…
A set of novel approaches for estimating epistemic uncertainty in deep neural networks with a single forward pass has recently emerged as a valid alternative to Bayesian Neural Networks. On the premise of informative representations, these…
The formalization of existing mathematical proofs is a notoriously difficult process. Despite decades of research on automation and proof assistants, writing formal proofs remains arduous and only accessible to a few experts. While previous…
We consider Incentive Decision Processes, where a principal seeks to reduce its costs due to another agent's behavior, by offering incentives to the agent for alternate behavior. We focus on the case where a principal interacts with a…
We introduce a new concept of approximation applicable to decision problems and functions, inspired by Bayesian probability. From the perspective of a Bayesian reasoner with limited computational resources, the answer to a problem that…
The efficiency of modern optimization methods, coupled with increasing computational resources, has led to the possibility of real-time optimization algorithms acting in safety critical roles. There is a considerable body of mathematical…
Online decision making under uncertainty in partially observable domains, also known as Belief Space Planning, is a fundamental problem in robotics and Artificial Intelligence. Due to an abundance of plausible future unravelings,…
We present a prototype of an integrated reasoning environment for educational purposes. The presented tool is a fragment of a proof assistant and automated theorem prover. We describe the existing and planned functionality of the theorem…
Symbolic regression is a powerful system identification technique in industrial scenarios where no prior knowledge on model structure is available. Such scenarios often require specific model properties such as interpretability, robustness,…