Related papers: Formally Verified Samplers From Probabilistic Prog…
Probabilistic programming provides a convenient lingua franca for writing succinct and rigorous descriptions of probabilistic models and inference tasks. Several probabilistic programming languages, including Anglican, Church or Hakaru,…
Formally verifying properties of programs that manipulate arrays in loops is computationally challenging. In this paper, we focus on a useful class of such programs, and present a novel property-driven verification method that first infers…
Program verification is to develop the program's proof system, and to prove the proof system soundness with respect to a trusted operational semantics of the program. However, many practical program verifiers are not based on operational…
We study a syntax for specifying quantitative "assertions" - functions mapping program states to numbers - for probabilistic program verification. We prove that our syntax is expressive in the following sense: Given any probabilistic…
Proof by coupling is a classical proof technique for establishing probabilistic properties of two probabilistic processes, like stochastic dominance and rapid mixing of Markov chains. More recently, couplings have been investigated as a…
For performance and verification in machine learning, new methods have recently been proposed that optimise learning systems to satisfy formally expressed logical properties. Among these methods, differentiable logics (DLs) are used to…
A variation of Gallager error-correcting codes is investigated using statistical mechanics. In codes of this type, a given message is encoded into a codeword which comprises Boolean sums of message bits selected by two randomly constructed…
Being able to soundly estimate roundoff errors of finite-precision computations is important for many applications in embedded systems and scientific computing. Due to the discrepancy between continuous reals and discrete finite-precision…
Conformal prediction has shown spurring performance in constructing statistically rigorous prediction sets for arbitrary black-box machine learning models, assuming the data is exchangeable. However, even small adversarial perturbations…
Incorrect handling of security-critical data formats, particularly in low-level languages, are the root cause of many security vulnerabilities. Provably correct parsing and serialization tools that target languages like C can help. Towards…
We present a formally verified framework for patent analysis as a hybrid AI + Lean 4 pipeline. The DAG-coverage core (Algorithm 1b) is fully machine-verified once bounded match scores are fixed. Freedom-to-operate, claim-construction…
Verified compilation of open modules (i.e., modules whose functionality depends on other modules) provides a foundation for end-to-end verification of modular programs ubiquitous in contemporary software. However, despite intensive…
We present a logical system CFP (Concurrent Fixed Point Logic) supporting the extraction of nondeterministic and concurrent programs that are provably total and correct. CFP is an intuitionistic first-order logic with inductive and…
A key problem in constrained random verification (CRV) concerns generation of input stimuli that result in good coverage of the system's runs in targeted corners of its behavior space. Existing CRV solutions however provide no formal…
We propose a sound and complete proof rule ProbTA for quantitative analysis of violation probability of probabilistic programs. Our approach extends the technique of trace abstraction with probability in the control-flow randomness style,…
This paper describes a formalization of discrete real closed fields in the Coq proof assistant. This abstract structure captures for instance the theory of real algebraic numbers, a decidable subset of real numbers with good algorithmic…
We present Lilac, a separation logic for reasoning about probabilistic programs where separating conjunction captures probabilistic independence. Inspired by an analogy with mutable state where sampling corresponds to dynamic allocation, we…
Conformal prediction (CP) is widely presented as distribution-free predictive inference with finite-sample marginal coverage under exchangeability. We argue that CP is best understood as a rank-calibrated descendant of the…
Large language models (LLMs) need reliable test-time control of hallucinations. Existing conformal methods for LLMs typically provide only \emph{marginal} guarantees and rely on a single global threshold, which can under-cover hard prompts,…
Gaussian processes are notorious for scaling cubically with the size of the training set, preventing application to very large regression problems. Computation-aware Gaussian processes (CAGPs) tackle this scaling issue by exploiting…