Related papers: Quantum proof systems for iterated exponential tim…
We present the first protocol allowing a classical computer to interactively verify the result of an efficient quantum computation. We achieve this by constructing a measurement protocol, which enables a classical verifier to use a quantum…
Reasoning under uncertainty is a fundamental challenge in Artificial Intelligence. As with most of these challenges, there is a harsh dilemma between the expressive power of the language used, and the tractability of the computational…
Probabilistic solvers provide a flexible and efficient framework for simulation, uncertainty quantification, and inference in dynamical systems. However, like standard solvers, they suffer performance penalties for certain stiff systems,…
Formal verification of neuro-symbolic cyber-physical systems, such as drones, medical devices and robots, is complicated. Neural components must be trained to be optimal with respect to the available data as well as the safety…
We prove a deterministic exponential time upper bound for Quantum Merlin-Arthur games with k unentangled provers. This is the first non-trivial upper bound of QMA(k) better than NEXP and can be considered an exponential improvement, unless…
Let $X=X_1\sqcup X_2\sqcup\ldots\sqcup X_k$ be a partitioned set of variables such that the variables in each part $X_i$ are noncommuting but for any $i\neq j$, the variables $x\in X_i$ commute with the variables $x'\in X_j$. Given as input…
Self-testing is a method to characterise an arbitrary quantum system based only on its classical input-output correlations, and plays an important role in device-independent quantum information processing as well as quantum complexity…
We propose a new algorithm for computing validated bounds for the solutions to the first order variational equations associated to ODEs. These validated solutions are the kernel of numerics computer-assisted proofs in dynamical systems…
Secure multi-party computation (MPC) is a general cryptographic technique that allows distrusting parties to compute a function of their individual inputs, while only revealing the output of the function. It has found applications in areas…
We prove the existence of (one-way) communication tasks with a subconstant versus superconstant asymptotic gap, which we call "doubly infinite," between their quantum information and communication complexities. We do so by studying the…
In an empirical study of persuasion, researchers often use a binary instrument to encourage individuals to consume information and take some action. We show that, with a binary Imbens-Angrist instrumental variable model and the monotone…
Agentic theorem provers combine a reasoning model, retrieval, search, and a proof assistant verifier, yet it remains unclear which components actually improve finite-budget proof success and why they help on real mathematical workloads. We…
Probabilities of the outcomes of consecutive quantum measurements can be obtained by construction probability amplitudes, thus implying unitary evolution of the measured system, broken each time a measurement is made. In practice, the…
While loops are present in virtually all imperative programming languages. They are important both for practical reasons (performing a number of iterations not known in advance) and theoretical reasons (achieving Turing completeness). In…
A fundamental challenge in formal theorem proving by LLMs is the lack of high-quality training data. Although reinforcement learning or expert iteration partially mitigates this issue by alternating between LLM generating proofs and…
We present an information theoretic proof of the nonsignalling multiprover parallel repetition theorem, a recent extension of its two-prover variant that underlies many hardness of approximation results. The original proofs used de Finetti…
We present a straightforward embedding of quantified multimodal logic in simple type theory and prove its soundness and completeness. Modal operators are replaced by quantification over a type of possible worlds. We present simple…
In this paper, we introduce a new public quantum interactive proof system and the first quantum alternating Turing machine: qAM proof system and qATM, respectively. Both are obtained from their classical counterparts (Arthur-Merlin proof…
Continuous representation of words is a standard component in deep learning-based NLP models. However, representing a large vocabulary requires significant memory, which can cause problems, particularly on resource-constrained platforms.…
We develop combinatorial test generation algorithms for progressively more powerful theorem provers, covering formula languages ranging from the implicational fragment of intuitionistic logic to full intuitionistic propositional logic. Our…