Related papers: Efficient Rational Proofs with Strong Utility-Gap …
We extend the theoretical framework of proof mining by establishing general logical metatheorems that allow for the extraction of the computational content of theorems with prima facie "non-computational" proofs from probability theory,…
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…
Informal arguments that cryptographic protocols are secure can be made rigorous using inductive definitions. The approach is based on ordinary predicate calculus and copes with infinite-state systems. Proofs are generated using…
Population protocols are a model of distributed computation intended for the study of networks of independent computing agents with dynamic communication structure. Each agent has a finite number of states, and communication opportunities…
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…
Fair termination is the property of programs that may diverge "in principle" but that terminate "in practice", i.e. under suitable fairness assumptions concerning the resolution of non-deterministic choices. We study a conservative…
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…
In this dissertation we collect some results about "interactive realizability", a realizability semantics that extends the Brouwer-Heyting-Kolmogorov interpretation to (sub-)classical logic, more precisely to first-order intuitionistic…
Recent advancements in Large Language Models (LLMs) have significantly enhanced their ability to perform complex reasoning tasks, transitioning from fast and intuitive thinking (System 1) to slow and deep reasoning (System 2). While System…
Recent advancements in large reasoning models (LRMs) have significantly enhanced language models' capabilities in complex problem-solving by emulating human-like deliberative thinking. However, these models often exhibit overthinking (i.e.,…
A key functionality of emerging connected autonomous systems such as smart cities, smart transportation systems, and the industrial Internet-of-Things, is the ability to process and learn from data collected at different physical locations.…
Interactive theorem provers such as Coq are powerful tools to formally guarantee the correctness of software. However, using these tools requires significant manual effort and expertise. While Large Language Models (LLMs) have shown promise…
Formal verification using interactive theorem provers ensures high-quality software. However, writing proof scripts for interactive theorem provers is labor-intensive and requires deep expertise. Recent studies have leveraged deep learning…
High-quality chain-of-thought has demonstrated strong potential for unlocking the reasoning capabilities of large language models. However, current paradigms typically treat the reasoning process as an indivisible sequence, lacking an…
The safety of automated driving systems must be justified by convincing arguments and supported by compelling evidence to persuade certification agencies, regulatory entities, and the general public to allow the systems on public roads.…
The syntactic nature of logic and computation separates them from other fields of mathematics. Nevertheless, syntax has been the only way to adequately capture the dynamics of proofs and programs such as cut-elimination, and the finiteness…
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…
Large language models increasingly rely on long chains of thought to improve accuracy, yet such gains come with substantial inference-time costs. We revisit token-efficient post-training and argue that existing sequence-level reward-shaping…
With recent progress on experimental quantum information processing, an important question has arisen as to whether it is possible to verify arbitrary computation performed on a quantum processor. A number of protocols have been proposed to…
The security of most existing cryptocurrencies is based on a concept called Proof-of-Work, in which users must solve a computationally hard cryptopuzzle to authorize transactions (`one unit of computation, one vote'). This leads to enormous…