Related papers: Automatic Complexity Analysis of Integer Programs …
Final-answer-based metrics are commonly used for evaluating large language models (LLMs) on math word problems, often taken as proxies for reasoning ability. However, such metrics conflate two distinct sub-skills: abstract formulation…
Reachable set computation is an important tool for analyzing control systems. Simulating a control system can show general trends, but a formal tool like reachability analysis can provide guarantees of correctness. Reachability analysis for…
A quantum annealer exploits quantum effects to solve a particular type of optimization problem. The advantage of this specialized hardware is that it effectively considers all possible solutions in parallel, thereby potentially…
A well-established approach to reasoning about loops during program analysis is to capture the effect of a loop by extracting recurrences from the loop; these express relationships between the values of variables, or program properties such…
Mixed integer nonlinear programs (MINLPs) are arguably among the hardest optimization problems, with a wide range of applications. MINLP solvers that are based on linear relaxations and spatial branching work similar as mixed integer…
In this paper, we study quantitative properties of quantum programs. Properties of interest include (positive) almost-sure termination, expected runtime or expected cost, that is, for example, the expected number of applications of a given…
Checking for Non-Termination (NT) of a given program P, i.e., determining if P has at least one non-terminating run, is an undecidable problem that continues to garner significant research attention. While unintended NT is common in…
Retrograde analysis reads programs from the end to the beginning: treat statements as constraints on prior states, propagate sets of states backward, and compare the reachable inputs with the intended specification. This tutorial condenses…
Any quantum program on a realistic quantum device must be compiled into an executable form while taking into account the underlying hardware constraints. Stringent restrictions on architecture and control imposed by physical platforms make…
One of the major limitations for the employment of model-based planning and scheduling in practical applications is the need of costly re-planning when an incongruence between the observed reality and the formal model is encountered during…
We give an approximation algorithm for packing and covering linear programs (linear programs with non-negative coefficients). Given a constraint matrix with n non-zeros, r rows, and c columns, the algorithm computes feasible primal and dual…
In this paper, we study systematically scalar one-loop two-, three-, and four-point Feynman integrals with complex internal masses. Our analytic results presented in this report are valid for both real and complex internal masses. The…
We study a class of functional problems reducible to computing $f^{(n)}(x)$ for inputs $n$ and $x$, where $f$ is a polynomial-time bijection. As we prove, the definition is robust against variations in the type of reduction used in its…
We study the problem of developing efficient approaches for proving worst-case bounds of non-deterministic recursive programs. Ranking functions are sound and complete for proving termination and worst-case bounds of nonrecursive programs.…
Given the limitations of current hardware, the theoretical gains promised by quantum computing remain unrealized across practical applications. But the gap between theory and hardware is closing, assisted by developments in quantum…
Automatically generating invariants, key to computer-aided analysis of probabilistic and deterministic programs and compiler optimisation, is a challenging open problem. Whilst the problem is in general undecidable, the goal is settled for…
There exist many Runge-Kutta methods (explicit or implicit), more or less adapted to specific problems. Some of them have interesting properties, such as stability for stiff problems or symplectic capability for problems with energy…
Programming is about automation in a wide variety of domains. Developing itself is one of those. As a side-effect, progress in automated coding may make people less willing to learn computer programming. This could become an issue, if the…
We describe three algorithms for computer-aided symbolic multi-loop calculations that facilitated some recent novel results. First, we discuss an algorithm to derive the canonical form of an arbitrary Feynman integral in order to facilitate…
Neural networks (NNs) are now routinely implemented on systems that must operate in uncertain environments, but the tools for formally analyzing how this uncertainty propagates to NN outputs are not yet commonplace. Computing tight bounds…