Related papers: Pegasus: Sound Continuous Invariant Generation

Loop invariants play a central role in the verification of imperative programs. However, finding these invariants is often a difficult and time-consuming task for the programmer. We have previously shown how program transformation can be…

Verification of programs operating on heap-allocated data structures, for instance lists or trees, poses significant challenges due to the potentially unbounded size of such data structures. We present time-indexed heap invariants, a novel…

Ensuring software correctness remains a fundamental challenge in formal program verification. One promising approach relies on finding polynomial invariants for loops. Polynomial invariants are properties of a program loop that hold before…

Safety Case has become an integral component for safety-certification in various Cyber Physical System domains including automotive, aviation, medical devices, and military. The certification processes for these systems are stringent and…

We develop a general framework for numerically solving differential equations while preserving invariants. As in standard projection methods, we project an arbitrary base integrator onto an invariant-preserving manifold, however, our method…

This paper studies runtime monitoring for persistent surveillance by autonomous robots when the autonomy stack is a black box. The environment is partitioned into finitely many parts, each carrying an uncertainty state that decreases when…

In this paper we study a class of dynamical systems generated by iterations of multivariate permutation polynomial systems which lead to polynomial growth of the degrees of these iterations. Using these estimates and the same techniques…

Controllers for dynamical systems that operate in safety-critical settings must account for stochastic disturbances. Such disturbances are often modeled as process noise in a dynamical system, and common assumptions are that the underlying…

Diffusion models are instrumental in text-to-audio (TTA) generation. Unfortunately, they suffer from slow inference due to an excessive number of queries to the underlying denoising network per generation. To address this bottleneck, we…

While end-to-end lyrics-to-song models offer convenience for casual users, professional songwriters require score-to-song systems that allow them to retain authorship over the core melody. However, existing score-to-song methods are limited…

One of the obstacles in automatic program proving is to obtain suitable loop invariants. The invariant of a loop is a weakened form of its postcondition (the loop's goal, also known as its contract); the present work takes advantage of this…

With recent breakthroughs in the construction of good qLDPC codes and nearly good qLTCs, the study of (co)homological invariants of quantum code complexes, which fundamentally underlie their logical operations, has become evidently…

Binaural audio plays a significant role in constructing immersive augmented and virtual realities. As it is expensive to record binaural audio from the real world, synthesizing them from mono audio has attracted increasing attention. This…

Autonomous Driving Systems (ADSs) rely on Deep Neural Networks, allowing vehicles to navigate complex, open environments. However, the unpredictability of these scenarios highlights the need for rigorous system-level testing to ensure…

Loop invariants are properties of a program loop that hold both before and after each iteration of the loop. They are often used to verify programs and ensure that algorithms consistently produce correct results during execution.…

Decoherence-free subsystems have been successfully developed as a tool to preserve fragile quantum information against noises. In this letter, we develop a structure theory for decoherence-free subsystems. Based on it, we present an…

We develop deep Poisson-gamma dynamical systems (DPGDS) to model sequentially observed multivariate count data, improving previously proposed models by not only mining deep hierarchical latent structure from the data, but also capturing…

Traditional synchronous STEM assessments face growing challenges including accessibility barriers, security concerns from resource-sharing platforms, and limited comparability across institutions. We present a framework for generating and…

Among the various critical systems that worth to be formally analyzed, a wide set consists of controllers for dynamical systems. Those programs typically execute an infinite loop in which simple com putations update internal states and…

Probabilistic programs are key to deal with uncertainty in e.g. controller synthesis. They are typically small but intricate. Their development is complex and error prone requiring quantitative reasoning over a myriad of alternative…