Related papers: Experience with Heuristics, Benchmarks & Standards…
While recent progress in quantum hardware open the door for significant speedup in certain key areas, quantum algorithms are still hard to implement right, and the validation of such quantum programs is a challenge. Early attempts either…
Cylindrical algebraic decomposition(CAD) is a key tool in computational algebraic geometry, particularly for quantifier elimination over real-closed fields. When using CAD, there is often a choice for the ordering placed on the variables.…
Solving symbolic reasoning problems that require compositionality and systematicity is considered one of the key ingredients of human intelligence. However, symbolic reasoning is still a great challenge for deep learning models, which often…
Cylindrical algebraic decomposition is a classical construction in real algebraic geometry. Although there are many algorithms to compute a cylindrical algebraic decomposition, their practical performance is still very limited. In this…
We present a systematic, algebraically based, design methodology for efficient implementation of computer programs optimized over multiple levels of the processor/memory and network hierarchy. Using a common formalism to describe the…
The algorithms employed by our communities are often underspecified, and thus have multiple implementation choices, which do not effect the correctness of the output, but do impact the efficiency or even tractability of its production. In…
Cylindrical Algebraic Decomposition (CAD) is an important tool within computational real algebraic geometry, capable of solving many problems for polynomial systems over the reals. It has long been studied by the Symbolic Computation…
AI has made significant progress in solving math problems, but geometry problems remain challenging due to their reliance on both text and diagrams. In the text description, symbolic characters such as "$\triangle$ABC" often serve as a…
Constructing complex computation from simpler building blocks is a defining problem of computer science. In algebraic automata theory, we represent computing devices as semigroups. Accordingly, we use mathematical tools like products and…
In the field of scientific computing, one often finds several alternative software packages (with open or closed source code) for solving a specific problem. These packages sometimes even use alternative methodological approaches, e.g.,…
Increased demands in the field of scientific computation require that algorithms be more efficiently implemented. Maintaining correctness in addition to efficiency is a challenge that software engineers in the field have to face. In this…
The neural network has become an integral part of modern software systems. However, they still suffer from various problems, in particular, vulnerability to adversarial attacks. In this work, we present a novel program reasoning framework…
Clustering is a fundamental technique in data analysis and machine learning, used to group similar data points together. Among various clustering methods, the Minimum Sum-of-Squares Clustering (MSSC) is one of the most widely used. MSSC…
Symbolic Regression (SR) is a powerful technique for discovering interpretable mathematical expressions. However, benchmarking SR methods remains challenging due to the diversity of algorithms, datasets, and evaluation criteria. In this…
The Conflict-Driven Cylindrical Algebraic Covering algorithm has proven well suited for performing theory validation checks in the satisfiability modulo theories paradigm for non-linear real arithmetic. CDCAC repurposes the theory…
Computing spherical harmonic decompositions is a ubiquitous technique that arises in a wide variety of disciplines and a large number of scientific codes. Because spherical harmonics are defined by integrals over spheres, however, one must…
Learning representations of algorithms is an emerging area of machine learning, seeking to bridge concepts from neural networks with classical algorithms. Several important works have investigated whether neural networks can effectively…
The role of mental simulation in human physical reasoning is widely acknowledged, but whether it is employed across scenarios with varying simulation costs and where its boundary lies remains unclear. Using a pouring-marble task, our human…
Dashboards are no longer mere static displays of metrics; through functionality such as interaction and storytelling, they have evolved to support analytic and communicative goals like monitoring and reporting. Existing dashboard design…
Answering Conjunctive Queries (CQs) and solving Constraint Satisfaction Problems (CSPs) are arguably among the most fundamental tasks in Computer Science. They are classical NP-complete problems. Consequently, the search for tractable…