Abstract We present an empirical study on the ability of Large Language Models (LLMs) to understand code by detecting semantically equivalent and inequivalent programs, that is, whether they compute the same result given the same input or not. To probe this, we deliberately perturb the program text by introducing semantics-preserving code transformations, namely copy propagation and constant folding. Using a benchmark of 11 Python functions with both equivalent and non-equivalent variants, we evaluate seven state-of-the-art LLMs (including ChatGPT, Claude, Gemini, and Deep-Seek) under zero-shot prompting, with and without minimal context. Despite strong performance in code generation tasks, the models often fail in this deeper reasoning challenge, misclassifying 41% of equivalent cases without context and 29% with context. Although prompting can improve performance, it does not address the underlying limitations of the models. We argue that improving LLMs themselves, through targeted fine-tuning, contrastive learning on equivalent and nonequivalent implementations, or training on transformation-invariant code, will be necessary for robust semantic understanding. Meanwhile, practitioners can achieve better results by selecting stronger models, carefully engineering prom-pts, or writing code with tools that normalize low-level differences before inference.

Advancements in Neural Networks have led to larger models, challenging implementation on embedded devices with memory, battery, and computational constraints. Consequently, network compression has flourished, offering solutions to reduce operations and parameters. However, many methods rely on heuristics, often requiring re-training for accuracy. Model reduction techniques extend beyond Neural Networks, relevant in Verification and Performance Evaluation fields. This paper bridges widely-used reduction strategies with formal concepts like lumpability, designed for analyzing Markov Chains. We propose a pruning approach based on lumpability, preserving exact behavioral outcomes without data dependence or fine-tuning. Relaxing strict quotienting method definitions enables a formal understanding of common reduction techniques.

Within modern Deep Learning setups, data augmentation is the weapon of choice when dealing with narrow datasets or with a poor range of different samples. However, the benefits of data augmentation are abysmal when applied to a dataset which is inherently unable to cover all the categories to be classified with a significant number of samples. To deal with such desperate scenarios, we propose a possible last resort: Cross-Dataset Data Augmentation. That is, the creation of new samples by morphing observations from a different source into credible specimens for the training dataset. Of course specific and strict conditions must be satisfied for this trick to work. In this paper we propose a general set of strategies and rules for Cross-Dataset Data Augmentation and we demonstrate its feasibility over a concrete case study. Even without defining any new formal approach, we think that the preliminary results of our paper are worth to produce a broader discussion on this topic.

Among several structured light approaches, phase shift is the most widely adopted in real-world 3D reconstruction devices. This is mainly due to its high accuracy, strong resilience to noise and straightforward implementation. However, Phase shift also exhibits an inherent weakness, that is the spatial ambiguity resulting from the periodicity of the sinusoidal wave adopted. Of course many phase unwrapping methods have been proposed to solve such ambiguity. One of the most promising methods exploits additional signals of mutually prime periods, in order to observe a distinct combination of phases for each spatial point. Unfortunately, for such combination to be properly recognized, a very high accuracy in phase recovery must be attained for each signal. In fact, even modest errors could lead to unwrapping faults, making the overall approach much less resilient to noise than plain phase shift. With this paper we introduce a feasible and effective fault recovery method that can be directly applied to multi-period phase shift. The combined pipeline offers an optimal accuracy and coverage even with high noise conditions, overcoming the setbacks of the original method. The performance of such pipeline is established by means of an in depth set of experimental evaluations and comparison, both with real and synthetically generated data.