Related papers: About Code Equivalence -- a Geometric Approach
Quantum programs exhibit inherent non-deterministic behavior, which poses more significant challenges for error discovery compared to classical programs. While several testing methods have been proposed for quantum programs, they often…
An approach to the equivalence problem of vector valued maps is offered which, in particular, covers the equivalence problem of paths and patches of differential geometry with respect to different motion groups. In the last case, in…
Linear logic Concurrent Constraint programming (LCC) is an extension of concurrent constraint programming (CC) where the constraint system is based on Girard's linear logic instead of the classical logic. In this paper we address the…
In this paper we introduce a measure of genuine quantum incompatibility in the estimation task of multiple parameters, that has a geometric character and is backed by a clear operational interpretation. This measure is then applied to some…
MapReduce frameworks are widely used for the implementation of distributed algorithms. However, translating imperative algorithms into these frameworks requires significant structural changes to the algorithm. As the costs of running faulty…
Many systems of interest to control engineering can be modeled by linear complementarity problems. We introduce a new notion of equivalence between linear complementarity problems that sets the basis to translate the powerful tools of…
Quantum information processors need to be protected against errors and faults. One of the most widely considered fault-tolerant architecture is based on surface codes. While the general principles of these codes are well understood and…
With an eye on developing a quantum theory of gravity, many physicists have recently searched for quantum challenges to the equivalence principle of general relativity. However, as historians and philosophers of science are well aware, the…
We introduce a new technique for solving uni-parametric versions of linear programs, convex quadratic programs, and linear complementarity problems in which a single parameter is permitted to be present in any of the input data. We…
This paper is devoted to the investigation of selected situations when the computation of projective (and other) equivalences of algebraic varieties can be efficiently solved with the help of finding projective equivalences of finite sets…
Many promising quantum algorithms in economics, medical science, and material science rely on circuits that are parameterized by a large number of angles. To ensure that these algorithms are efficient, these parameterized circuits must be…
Achieving fault-tolerance will require a strong relationship between the hardware and the protocols used. Different approaches will therefore naturally have tailored proof-of-principle experiments to benchmark progress. Nevertheless,…
This work is meant to be a step towards the formal definition of the notion of algorithm, in the sense of an equivalence class of programs working "in a similar way". But instead of defining equivalence transformations directly on programs,…
The problem of checking whether two programs are semantically equivalent or not has a diverse range of applications, and is consequently of substantial importance. There are several techniques that address this problem, chiefly by…
Program code contains functions, variables, and data structures that are represented by names. To promote human understanding, these names should describe the role and use of the code elements they represent. But the names given by…
Program equivalence in linear contexts, where programs are used or executed exactly once, is an important issue in programming languages. However, existing techniques like those based on bisimulations and logical relations only target at…
In this text we develop the formalism of products and powers of linear codes under componentwise multiplication. As an expanded version of the author's talk at AGCT-14, focus is put mostly on basic properties and descriptive statements that…
Linearizability is a commonly accepted notion of correctness for libraries of concurrent algorithms, and recent years have seen a number of proposals of program logics for proving it. Although these logics differ in technical details, they…
Formal verification is the next frontier for ensuring the correctness of code generated by Large Language Models (LLMs). While methods that co-generate code and formal specifications in formal languages, like Dafny, can, in principle, prove…
Several application domains require formal but flexible approaches to the comparison problem. Different process models that cannot be related by behavioral equivalences should be compared via a quantitative notion of similarity, which is…