Related papers: Coupling proofs are probabilistic product programs

Coding theory is very useful for real world applications. A notable example is digital television. Basically, coding theory is to study a way of detecting and/or correcting data that may be true or false. Moreover coding theory is an area…

This paper surveys recent work on applying analysis and transformation techniques that originate in the field of constraint logic programming (CLP) to the problem of verifying software systems. We present specialisation-based techniques for…

Probabilistic separation logic offers an approach to reasoning about imperative probabilistic programs in which a separating conjunction is used as a mechanism for expressing independence properties. Crucial to the effectiveness of the…

LLMs are widely used for code generation and mathematical reasoning tasks where they are required to generate structured output. They either need to reason about code, generate code for a given specification, or reason using programs of…

We consider the problem of how to verify the security of probabilistic oblivious algorithms formally and systematically. Unfortunately, prior program logics fail to support a number of complexities that feature in the semantics and…

Many machine learning applications require the ability to learn from and reason about noisy multi-relational data. To address this, several effective representations have been developed that provide both a language for expressing the…

In various provers and deductive verification tools, logical transformations are used extensively in order to reduce a proof task into a number of simpler tasks. Logical transformations are often part of the trusted base of such tools. In…

Recursive calls over recursive data are useful for generating probability distributions, and probabilistic programming allows computations over these distributions to be expressed in a modular and intuitive way. Exact inference is also…

Particle filters are a powerful and flexible tool for performing inference on state-space models. They involve a collection of samples evolving over time through a combination of sampling and re-sampling steps. The re-sampling step is…

Program synthesis--the automated generation of executable code from high-level specifications--has been a central goal of computer science for over fifty years. This thesis provides a comparative literature review of the main paradigms that…

Cyber-physical systems (CPS) such as autonomous cars, aircraft, and robots are often also safety-critical; thus it is imperative that they operate as intended with a high degree of certainty. Formal verification has been employed to verify…

Array-intensive programs are often amenable to parallelization across many cores on a single machine as well as scaling across multiple machines and hence are well explored, especially in the domain of high-performance computing. These…

We consider the task of performing probabilistic inference with probabilistic logical models. Many algorithms for approximate inference with such models are based on sampling. From a logic programming perspective, sampling boils down to…

We present Proof-of-Perception (PoP), a tool-using framework that casts multimodal reasoning as an executable graph with explicit reliability guarantees. Each perception or logic node outputs a conformal set, yielding calibrated, stepwise…

Training language models to solve complex mathematical problems benefits from curriculum learning progressively training on simpler subproblems. However, existing decomposition methods are often heuristic, offering no guarantees that…

While probability theory is normally applied to external environments, there has been some recent interest in probabilistic modeling of the outputs of computations that are too expensive to run. Since mathematical logic is a powerful tool…

Our research is part of a wider project that aims to investigate and reason about the correctness of scheme-based source code transformations of Erlang programs. In order to formally reason about the definition of a programming language and…

Plausible reasoning concerns situations whose inherent lack of precision is not quantified; that is, there are no degrees or levels of precision, and hence no use of numbers like probabilities. A hopefully comprehensive set of principles…

Matching logic is a formalism for specifying, and reasoning about, mathematical structures, using patterns and pattern matching. Growing in popularity, it has been used to define many logical systems such as separation logic with recursive…

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…