Related papers: Verifying Asymptotic Time Complexity of Imperative…
When deploying LLMs in agentic architectures requiring real-time decisions under temporal constraints, we assume they reliably determine whether action windows remain open or have closed. This assumption is untested. We characterize…
We present a method for synthesizing recursive functions that satisfy both a functional specification and an asymptotic resource bound. Prior methods for synthesis with a resource metric require the user to specify a concrete expression…
Convergence properties of model-free two-timescale asymptotic simulations of singularly perturbed hybrid inclusions are developed. A hybrid inclusion combines constrained differential and difference inclusions to capture continuous (flow)…
The Asymptotic Iteration Method (AIM) is a technique for solving analytically and approximately the linear second-order differential equation, especially the eigenvalue problems that frequently appear in theoretical and mathematical…
This paper contains two results on timed extensions of pushdown automata (PDA). As our first result we prove that the model of dense-timed PDA of Abdulla et al. collapses: it is expressively equivalent to dense-timed PDA with timeless…
`What more than its truth do we know if we have a proof of a theorem in a given formal system?' We examine Kreisel's question in the particular context of program termination proofs, with an eye to deriving complexity bounds on program…
Difference constraints have been used for termination analysis in the literature, where they denote relational inequalities of the form x' <= y + c, and describe that the value of x in the current state is at most the value of y in the…
We want to verify the correctness of optimization phases in the GraalVM compiler, which consist of many thousands of lines of complex Java code performing sophisticated graph transformations. We have built high-level models of the data…
We present a model-agnostic framework for the construction of prediction intervals of insurance claims, with finite sample statistical guarantees, extending the technique of split conformal prediction to the domain of two-stage…
Isabelle is an interactive theorem prover that supports a variety of logics. It represents rules as propositions (not as functions) and builds proofs by combining rules. These operations constitute a meta-logic (or `logical framework') in…
Formally verifying properties of software code has been a highly desirable task, especially with the emergence of LLM-generated code. In the same vein, they provide an interesting avenue for the exploration of formal verification and…
Autoregressive models are a class of time series models that are important in both applied and theoretical statistics. Typically, inferential devices such as confidence sets and hypothesis tests for time series models require nuanced…
In earlier work, we developed an approach for automatic complexity analysis of integer programs, based on an alternating modular inference of upper runtime and size bounds for program parts. In this paper, we show how recent techniques to…
This is an overview of the Isabelle technology behind the Archive of Formal Proofs (AFP). Interactive development and quasi-interactive build jobs impose significant demands of scalability on the logic (usually Isabelle/HOL), on Isabelle/ML…
In this Masters thesis we present an implementation of a fragment of "book HoTT" as an object logic for the interactive proof assistant Isabelle. We also give a mathematical description of the underlying theory of the Isabelle/Pure logical…
We mechanize, in the proof assistant Isabelle, a proof of the axiom-scheme of Separation in generic extensions of models of set theory by using the fundamental theorems of forcing. We also formalize the satisfaction of the axioms of…
Traditional algorithm analysis treats all basic operations as equally costly, which hides significant differences in time, energy consumption, and cost between different types of computations on modern processors. We propose a…
We develop a timeout based extension of propositional linear temporal logic (which we call TLTL) to specify timing properties of timeout based models of real time systems. TLTL formulas explicitly refer to a running global clock together…
Inductive theorem proving is an important long-standing challenge in computer science. In this extended abstract, we first summarize the recent developments of proof by induction for Isabelle/HOL. Then, we propose united reasoning, a novel…
Algorithmic interpretability is necessary to build trust, ensure fairness, and track accountability. However, there is no existing formal measurement method for algorithmic interpretability. In this work, we build upon programming language…