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We present a semi-automated framework to construct and reason about programs in a deeply-embedded while-language. The while-language we consider is a simple computation model that can simulate (and be simulated by) Turing Machines with a…
Most expressivity results for transformers treat them as language recognizers -- devices that accept or reject strings -- rather than as they are used in practice: as language models that generate strings autoregressively and…
The FermaT transformation system, based on research carried out over the last sixteen years at Durham University, De Montfort University and Software Migrations Ltd., is an industrial-strength formal transformation engine with many…
Reversible computing is a computational paradigm in which computations are deterministic in both the forward and backward direction, so that programs have well-defined forward and backward semantics. We investigate the formal semantics of…
The quantum cloner machine maps an unknown arbitrary input qubit into two optimal clones and one optimal flipped qubit. By combining linear and non-linear optical methods we experimentally implement a scheme that, after the cloning…
Algorithms are ways of mapping problems to solutions. An algorithm is invertible precisely when this mapping is injective, such that the initial problem can be uniquely inferred from its solution. While invertible algorithms can be…
We observe a large number of functions differing from each other only by a translation parameter. While the main pattern is unknown, we propose to estimate the shift parameters using $M$-estimators. Fourier transform enables to transform…
Given that in practice training data is scarce for all but a small set of problems, a core question is how to incorporate prior knowledge into a model. In this paper, we consider the case of prior procedural knowledge for neural networks,…
We investigate representations of imperative programs as constrained Horn clauses. Starting from operational semantics transition rules, we proceed by writing interpreters as constrained Horn clause programs directly encoding the rules. We…
Synthesizing programs from examples requires searching over a vast, combinatorial space of possible programs. In this search process, a key challenge is representing the behavior of a partially written program before it can be executed, to…
Recent work has shown that the computations of Transformers can be simulated in the RASP family of programming languages. These findings have enabled improved understanding of the expressive capacity and generalization abilities of…
We find limits to the Transformer architecture for language modeling and show it has a universal prediction property in an information-theoretic sense. We further analyze performance in non-asymptotic data regimes to understand the role of…
Refinement calculus provides a structured framework for the progressive and modular development of programs, ensuring their correctness throughout the refinement process. This paper introduces a refinement calculus tailored for quantum…
Transformers have had a significant impact on natural language processing and have recently demonstrated their potential in computer vision. They have shown promising results over convolution neural networks in fundamental computer vision…
Given a simple recursive function, we show how to extract from it a reversible and an classical iterative part. Those parts can synchronously cooperate under a Producer/Consumer pattern in order to implement the original recursive function.…
In this article, we discuss a flow--sensitive analysis of equality relationships for imperative programs. We describe its semantic domains, general purpose operations over abstract computational states (term evaluation and identification,…
This work examines approaches to making computational models reversible. Broadly speaking, transforming a computational model into a reversible one, i.e. reversibilizing it, means extending its operational semantics conservatively in a way…
The problem of inverting the total divergence operator is central to finding components of a given conservation law. This might not be taxing for a low-order conservation law of a scalar partial differential equation, but integrable systems…
We describe how to use refactoring tools to transform a Java program conforming to the Composite design pattern into a program conforming to the Visitor design pattern with the same external behavior. We also describe the inverse…
Efficient simulation of quantum computers is essential for the development and validation of near-term quantum devices and the research on quantum algorithms. Up to date, two main approaches to simulation were in use, based on either full…