Related papers: A Deductive Verification Infrastructure for Probab…
Modal logics allow reasoning about various modes of truth: for example, what it means for something to be possibly true, or to know that something is true as opposed to merely believing it. This report describes embeddings of propositional…
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,…
We present a simple and concise semantics for temporal planning. Our semantics are developed and formalised in the logic of the interactive theorem prover Isabelle/HOL. We derive from those semantics a validation algorithm for temporal…
Differential dynamic logic (dL) is a formal framework for specifying and reasoning about hybrid systems, i.e., dynamical systems that exhibit both continuous and discrete behaviors. These kinds of systems arise in many safety- and…
The rapid advancement of large language models (LLMs) has revolutionized code generation tasks across various programming languages. However, the unique characteristics of programming languages, particularly those like Verilog with specific…
We present a new inductive rule for verifying lower bounds on expected values of random variables after execution of probabilistic loops as well as on their expected runtimes. Our rule is simple in the sense that loop body semantics need to…
Relational program verification is a variant of program verification where one can reason about two programs and as a special case about two executions of a single program on different inputs. Relational program verification can be used for…
Valuation algebras abstract a large number of formalisms for automated reasoning and enable the definition of generic inference procedures. Many of these formalisms provide some notion of solution. Typical examples are satisfying…
Formal verification of complex algorithms is challenging. Verifying their implementations goes beyond the state of the art of current automatic verification tools and usually involves intricate mathematical theorems. Certifying algorithms…
Vision-language models (VLMs), such as CLIP, have gained popularity for their strong open vocabulary classification performance, but they are prone to assigning high confidence scores to misclassifications, limiting their reliability in…
Large language models (LLMs) have shown increasing competence in solving mathematical reasoning problems. However, many open-source LLMs still struggle with errors in calculation and semantic understanding during intermediate reasoning…
In this thesis, we present two approaches to a rigorous mathematical and algorithmic foundation of quantitative and statistical inference in constraint-based natural language processing. The first approach, called quantitative constraint…
Formal verification provides strong guarantees of correctness of software, which are especially important in safety or security critical systems. Hoare logic is a widely used formalism for rigorous verification of software against…
Deciding termination is a fundamental problem in the analysis of probabilistic imperative programs. We consider the qualitative and quantitative probabilistic termination problems for an imperative programming model with discrete…
This paper presents IsaBIL, a binary analysis framework in Isabelle/HOL that is based on the widely used Binary Analysis Platform (BAP). Specifically, in IsaBIL, we formalise BAP's intermediate language, called BIL and integrate it with…
Natural Language Processing is rapidly evolving into a primary instrument for Computational Social Science, with researchers increasingly using embeddings to measure latent constructs such as novelty, creativity, and bias. However, this…
The instrumental variables (IVs) method is a leading empirical strategy for causal inference. Finding IVs is a heuristic and creative process, and justifying its validity -- especially exclusion restrictions -- is largely rhetorical. We…
Quantitative separation logic (QSL) is an extension of separation logic (SL) for the verification of probabilistic pointer programs. In QSL, formulae evaluate to real numbers instead of truth values, e.g., the probability of memory-safe…
Probabilistic programs are a powerful and convenient approach to formalise distributions over system executions. A classical verification problem for probabilistic programs is temporal inference: to compute the likelihood that the execution…
Foundational verification considers the functional correctness of programming languages with formalized semantics and uses proof assistants (e.g., Coq, Isabelle) to certify proofs. The need for verifying complex programs compels it to…