Related papers: Time-Optimal Interactive Proofs for Circuit Evalua…
Theorem provers are important tools for people working in formal verification. There are a myriad of interactive systems available today, with varying features and approaches motivating their development. These design choices impact their…
This report describes the state of the art in verifiable computation. The problem being solved is the following: The Verifiable Computation Problem (Verifiable Computing Problem) Suppose we have two computing agents. The first agent is the…
Recent progress in formal theorem proving has benefited from large-scale proof generation and verifier-aware training, but agentic proving is rarely integrated into prover training, appearing only at inference time. We present OProver, a…
We introduce Prove-It, a Python-based general-purpose interactive theorem-proving assistant designed with the goal of making formal theorem proving as easy and natural as informal theorem proving (with moderate training). Prove-It uses a…
We continue the study of doubly-efficient proof systems for verifying agnostic PAC learning, for which we obtain the following results. - We construct an interactive protocol for learning the $t$ largest Fourier characters of a given…
Noisy data, non-convex objectives, model misspecification, and numerical instability can all cause undesired behaviors in machine learning systems. As a result, detecting actual implementation errors can be extremely difficult. We…
We present Cobra, a modern proof presentation framework, leveraging cutting-edge presentation technology together with a state of the art interactive theorem prover to present formalized mathematics as active documents. Cobra provides both…
Interactive program verification is characterized by iterations of unfinished proof attempts. To support the process of constructing a complete proof, many interactive program verification systems offer a proof scripting language as a…
Quantum inspired protocols e.g. [AAV13,AG17] attempt to achieve a single-prover interactive protocol where a classical machine can verify quantum computations in an information-theoretically secure manner. We define a family of protocols…
One of the elegant achievements in the history of proof theory is the characterization of the provably total recursive functions of an arithmetical theory by its proof-theoretic ordinal as a way to measure the time complexity of the…
We consider a setting where a verifier with limited computation power delegates a resource intensive computation task---which requires a $T\times S$ computation tableau---to two provers where the provers are rational in that each prover…
This comprehensive survey examines Lean 4, a state-of-the-art interactive theorem prover and functional programming language. We analyze its architectural design, type system, metaprogramming capabilities, and practical applications in…
In recent times, many protocols have been proposed to provide security for various information and communication systems. Such protocols must be tested for their functional correctness before they are used in practice. Application of formal…
We introduce pseudo-deterministic interactive proofs (psdAM): interactive proof systems for search problems where the verifier is guaranteed with high probability to output the same output on different executions. As in the case with…
Interrupts have been widely used in safety-critical computer systems to handle outside stimuli and interact with the hardware, but reasoning about interrupt-driven software remains a difficult task. Although a number of static verification…
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…
We present StepFun-Prover Preview, a large language model designed for formal theorem proving through tool-integrated reasoning. Using a reinforcement learning pipeline that incorporates tool-based interactions, StepFun-Prover can achieve…
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…
We show that any language in nondeterministic time $\exp(\exp(\cdots \exp(n)))$, where the number of iterated exponentials is an arbitrary function $R(n)$, can be decided by a multiprover interactive proof system with a classical…
Probing in mixed-integer programming (MIP) is a technique of temporarily fixing variables to discover implications that are useful to branch-and-cut solvers. Such fixing is typically performed one variable at a time -- this paper develops…