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Iterated functions system (IFS) is defined by specifying a set of functions in a classical phase space, which act randomly on an initial point. In an analogous way, we define a quantum iterated functions system (QIFS), where functions act…
We show that recent approaches of static analysis based on quantitative typing systems can be extended to programming languages with global state. More precisely, we define a call-by-value language equipped with operations to access a…
Dependently typed programming languages allow sophisticated properties of data to be expressed within the type system. Of particular use in dependently typed programming are indexed types that refine data by computationally useful…
We present the design, implementation, and foundation of a verifier for higher-order functional programs with generics and recursive data types. Our system supports proving safety and termination using preconditions, postconditions and…
Environmental noise (e.g.heat, ionized particles, etc.) causes transient faults in hardware, which lead to corruption of stored values. Mission-critical devices require such faults to be mitigated by fault-tolerance --- a combination of…
We describe an application of Prolog: a type checking tool for the Q functional language. Q is a terse vector processing language, a descendant of APL, which is getting more and more popular, especially in financial applications. Q is a…
We introduce idris-ct, a Idris library providing verified type definitions of categorical concepts.idris-ct strives to be a bridge between academy and industry, catering both to category theorists who want to implement and try their ideas…
Secure function computation has been thoroughly studied and optimized in the past decades. We extend techniques used for secure computation to simulate arbitrary protocols involving a mediator. The key feature of our notion of simulation is…
Broadly speaking Information theory (IT) assumes no structure of the underlying states. But what about contexts where states do have a clear structure - how should IT cope with such situations? And if such coping is at all possible then -…
Graph theory is important in information theory. We introduce a quantization process on graphs and apply the quantized graphs in quantum information. The quon language provides a mathematical theory to study such quantized graphs in a…
Training a general-purpose time series foundation models with robust generalization capabilities across diverse applications from scratch is still an open challenge. Efforts are primarily focused on fusing cross-domain time series datasets…
\emph{Session types} have proved viable in expressing and verifying the protocols of message-passing systems. While message passing is a dominant concurrency paradigm in practice, real world software is written without session types. A…
Many mathematical objects can be represented as functors from finitely-presented categories $\mathsf{C}$ to $\mathsf{Set}$. For instance, graphs are functors to $\mathsf{Set}$ from the category with two parallel arrows. Such functors are…
Global-type formalisms enable to describe the overall behaviour of distributed systems and at the same time to enforce safety properties for communications between system components. Our goal is that of amending a weakness of such…
Categories and categorical structures are increasingly recognized as useful abstractions for modeling in science and engineering. To uniformly implement category-theoretic mathematical models in software, we introduce GATlab, a…
Developing secure distributed systems is difficult, and even harder when advanced cryptography must be used to achieve security goals. Following prior work, we advocate using secure program partitioning to synthesize cryptographic…
We propose a method for inferring \emph{parameterized regular types} for logic programs as solutions for systems of constraints over sets of finite ground Herbrand terms (set constraint systems). Such parameterized regular types generalize…
Generalization is the ability of machine learning models to make accurate predictions on new data by learning from training data. However, understanding generalization of quantum machine learning models has been a major challenge. Here, we…
Process theories provide a powerful framework for describing compositional structures across diverse fields, from quantum mechanics to computational linguistics. Traditionally, they have been formalized using symmetric monoidal categories…
We propose a formal model of concurrent systems in which the history of a computation is explicitly represented as a collection of events that provide a view of a sequence of configurations. In our model events generated by transitions…