Related papers: An automatic system to detect equivalence between …
Many algorithms use data structures that maintain properties of matrices undergoing some changes. The applications are wide-ranging and include for example matchings, shortest paths, linear programming, semi-definite programming, convex…
Two curves are affinely equivalent if there exists an affine mapping transforming one of them onto the other. Thus, detecting affine equivalence comprises, as important particular cases, similarity, congruence and symmetry detection. In…
The preference optimization literature contains many proposed objectives, often presented as distinct improvements. We introduce Opal, a canonicalization algorithm that determines whether two preference objectives are algebraically…
Given two algorithms for the same problem, can we determine whether they are meaningfully different? In full generality, the question is uncomputable, and empirically it is muddied by competing notions of similarity. Yet, in many…
In this paper, we consider a quantum algorithm for solving the following problem: ``Suppose $f$ is a function given as a black box (that is also called an oracle) and $f$ is invariant under some AND-mask. Examine a property of $f$ by…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
The purpose of this paper is to introduce a concept of equivalence between machine learning algorithms. We define two notions of algorithmic equivalence, namely, weak and strong equivalence. These notions are of paramount importance for…
It is well understood that classification algorithms, for example, for deciding on loan applications, cannot be evaluated for fairness without taking context into account. We examine what can be learned from a fairness oracle equipped with…
Existing approaches to algorithmic fairness aim to ensure equitable outcomes if human decision-makers comply perfectly with algorithmic decisions. However, perfect compliance with the algorithm is rarely a reality or even a desirable…
Let A, B, C, D be given finite sets of pairs of n-by-n complex matrices. We describe an algorithm to determine, with finitely many computations, whether there is a single unitary matrix U such that each pair of matrices in A is unitarily…
Design methods in information systems frequently create software descriptions using formal languages. Nonetheless, most software designers prefer to describe software using natural languages. This distinction is not simply a matter of…
Given a loop or more generally 1-cycle $r$ of size L on a closed two-dimensional manifold or surface, represented by a triangulated mesh, a question in computational topology asks whether or not it is homologous to zero. We frame and tackle…
We introduce a novel framework for human-AI collaboration in prediction and decision tasks. Our approach leverages human judgment to distinguish inputs which are algorithmically indistinguishable, or "look the same" to any feasible…
We propose a scalable framework for deciding, proving, and explaining (in-)equivalence of context-free grammars. We present an implementation of the framework and evaluate it on large data sets collected within educational support systems.…
Distributed programs are often formulated in popular functional frameworks like MapReduce, Spark and Thrill, but writing efficient algorithms for such frameworks is usually a non-trivial task. As the costs of running faulty algorithms at…
Algorithms are the engine for reproducible problem-solving. We present a framework automating algorithm discovery by conceptualizing them as sequences of operations, represented as tokens. These computational tokens are chained using a…
Comparing, or benchmarking, of optimization algorithms is a complicated task that involves many subtle considerations to yield a fair and unbiased evaluation. In this paper, we systematically review the benchmarking process of optimization…
We target the problem of provably computing the equivalence between two complex expression trees. To this end, we formalize the problem of equivalence between two such programs as finding a set of semantics-preserving rewrite rules from one…
Intruders can infer properties of a system by measuring the time it takes for the system to respond to some request of a given protocol, that is, by exploiting time side channels. These properties may help intruders distinguish whether a…
The starting point of this work is a framework allowing to model systems with dynamic process creation, equipped with a procedure to detect symmetric executions (ie., which differ only by the identities of processes). This allows to reduce…