Related papers: Run-Based Semantics for RPQs
Foundation models in language and vision benefit from a unified discrete token interface that converts raw inputs into sequences for scalable pre-training and inference. For graphs, an effective tokenizer should yield reusable discrete…
Quantum and random walks have been shown to be equivalent in the following sense: a time-dependent random walk can be constructed such that its vertex distribution at all time instants is identical to the vertex distribution of any…
Quantum walks are a promising framework that can be used to both understand and implement quantum information processing tasks. The quantum stochastic walk is a recently developed framework that combines the concept of a quantum walk with…
Execution of concurrent programs implies frequent switching between different thread contexts. This property perplexes analyzing and reasoning about concurrent programs. Trace simplification is a technique that aims at alleviating this…
Quantum walks are a well-established model for the study of coherent transport phenomena and provide a universal platform in quantum information theory. Dynamically influencing the walker's evolution gives a high degree of flexibility for…
Random walks on graphs are widely used in all sciences to describe a great variety of phenomena where dynamical random processes are affected by topology. In recent years, relevant mathematical results have been obtained in this field, and…
Large reasoning models (LRMs) generate complex reasoning traces with planning, reflection, verification, and backtracking. In this work, we introduce ReasoningFlow, a unified schema for analyzing the semantic structures of these complex…
Quantum walks, being the quantum analogue of classical random walks, are expected to provide a fruitful source of quantum algorithms. A few such algorithms have already been developed, including the `glued trees' algorithm, which provides…
Graphs have emerged as an important foundation for a variety of applications, including capturing and reasoning over factual knowledge, semantic data integration, social networks, and providing factual knowledge for machine learning…
Cyclomatic complexity is an incompletely specified but mathematically principled software metric that can be usefully applied to both source and binary code. We consider the application of path homology as a stronger analogue of cyclomatic…
Quantum versions of random walks have diverse applications that are motivating experimental implementations as well as theoretical studies. However, the main impetus behind this interest is their use in quantum algorithms, which have always…
Relational data sources are still one of the most popular ways to store enterprise or Web data, however, the issue with relational schema is the lack of a well-defined semantic description. A common ontology provides a way to represent the…
Temporal logics have been studied as an approach to the specification of hyperproperties, resulting in the conception of "hyperlogics". With a few recent exceptions, the hyperlogics thus far developed can only relate different traces of a…
Graph-Convolution-based methods have been successfully applied to representation learning on homophily graphs where nodes with the same label or similar attributes tend to connect with one another. Due to the homophily assumption of Graph…
In this paper, we analyze the potential for new types of searches using the formalism of scattering random walks on Quantum Computers. Given a particular type of graph consisting of nodes and connections, a "Tree Maze", we would like to…
Large scale complex systems, such as social networks, electrical power grid, database structure, consumption pattern or brain connectivity, are often modeled using network graphs. Valuable insight can be gained by measuring the similarity…
SQL is the world's most popular declarative language, forming the basis of the multi-billion-dollar database industry. Although SQL has been standardized, the full standard is based on ambiguous natural language rather than formal…
This paper presents a language-independent proof system for reachability properties of programs written in non-deterministic (e.g., concurrent) languages, referred to as all-path reachability logic. It derives partial-correctness properties…
The World Wide Web currently evolves into a Web of Linked Data where content providers publish and link data as they have done with hypertext for the last 20 years. While the declarative query language SPARQL is the de facto for querying…
Transformers have become a central architecture for graph learning, but their application to graphs requires first choosing a tokenization: a graph-to-token map that determines which structural information is exposed at the input. In this…