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We introduce fidelity probes: natural-language questions generated from a reference artifact with code-derived ground-truth answers, answered from a candidate specification. The fraction of agreeing probes, which we call the fidelity,…
Single-layer Graphene (SLG) is a promising material for sensing applications. High performance graphene sensors can be achieved when Interdigitated Electrodes (IDE) are used. In this research work, we fabricated SLG micro-ribbon (GMR)…
Attaining fault tolerance while maintaining low overhead is one of the main challenges in a practical implementation of quantum circuits. One major technique that can overcome this problem is the flag technique, in which high-weight errors…
Graphs are a fundamental abstraction in computer science and discrete mathematics, where information is encoded in their combinatorial structure. Graph-reduction techniques aim at simplifying graphs while preserving selected structural…
We propose the first method to show theoretical limitations for one-layer softmax transformers with arbitrarily many precision bits (even infinite). We establish those limitations for three tasks that require advanced reasoning. The first…
The aim of this paper is to characterize an important class of marked digraphs, called structurally observable graphs (SOGs), and to solve two minimum realization problems. To begin with, by exploring structural observability of large-scale…
The list coloring problem is a variant of vertex coloring where a vertex may be colored only a color from a prescribed set. Several applications of vertex coloring are more appropriately modelled as instances of list coloring and thus we…
We study a variation of the graph colouring problem on random graphs of finite average connectivity. Given the number of colours, we aim to maximise the number of different colours at neighbouring vertices (i.e. one edge distance) of any…
When a low dimensional chaotic attractor is embedded in a three dimensional space its topological properties are embedding-dependent. We show that there are just three topological properties that depend on the embedding: parity, global…
A $k$-coloring of a tournament is a partition of its vertices into $k$ acyclic sets. Deciding if a tournament is 2-colorable is NP-hard. A natural problem, akin to that of coloring a 3-colorable graph with few colors, is to color a…
Vision-Language Models (VLMs) have become a central focus of today's AI community, owing to their impressive abilities gained from training on large-scale vision-language data from the Web. These models have demonstrated strong performance…
Large Language Models are increasingly deployed as judges (LaaJ) in code generation pipelines. While attractive for scalability, LaaJs tend to overlook domain specific issues raising concerns about their reliability in critical evaluation…
Considering the challenges faced by large language models (LLMs) in logical reasoning and planning, prior efforts have sought to augment LLMs with access to external solvers. While progress has been made on simple reasoning problems,…
Models of complex systems are widely used in the physical and social sciences, and the concept of layering, typically building upon graph-theoretic structure, is a common feature. We describe an intuitionistic substructural logic called…
A coloring is distinguishing (or symmetry breaking) if no non-identity automorphism preserves it. The distinguishing threshold of a graph $G$, denoted by $\theta(G)$, is the minimum number of colors $k$ so that every $k$-coloring of $G$ is…
Large language models have recently made great strides in reasoning task performance through chain-of-thought (CoT) strategies trained via reinforcement learning; however, these "reasoning large language models" (RLLMs) remain imperfect…
A central challenge in developing Multimodal Large Language Models (MLLMs) is effectively integrating heterogeneous inputs into a cohesive reasoning engine. Current paradigms predominantly rely on modular architectures that introduce…
In this paper, we suggest new SAT encodings of the partial-ordering based ILP model for the graph coloring problem (GCP) and the bandwidth coloring problem (BCP). The GCP asks for the minimum number of colors that can be assigned to the…
Logic locking aims to prevent intellectual property (IP) piracy and unauthorized overproduction of integrated circuits (ICs). However, initial logic locking techniques were vulnerable to the Boolean satisfiability (SAT)-based attacks. In…
We develop an algorithmic framework for graph colouring that reduces the problem to verifying a local probabilistic property of the independent sets. With this we give, for any fixed $k\ge 3$ and $\varepsilon>0$, a randomised…