Related papers: Catalytic Computing and Register Programs Beyond L…
In this paper, we study circuits and formulas for provenance polynomials of Datalog programs. We ask the following question: given an absorptive semiring and a fact of a Datalog program, what is the optimal depth and size of a…
Tsetlin machine (TM) is a logic-based machine learning approach with the crucial advantages of being transparent and hardware-friendly. While TMs match or surpass deep learning accuracy for an increasing number of applications, large clause…
The accelerating adoption of Large Language Models (LLMs) in software engineering (SE) has brought with it a silent crisis: unsustainable computational cost. While these models demonstrate remarkable capabilities in different SE tasks, they…
The ever-increasing parallelism demand of General-Purpose Graphics Processing Unit (GPGPU) applications pushes toward larger and more energy-hungry register files in successive GPU generations. Reducing the supply voltage beyond its safe…
Besides the Hidden Subgroup Problem, the second large class of quantum speed-ups is for functions with constant-sized 1-certificates. This includes the OR function, solvable by the Grover algorithm, the distinctness, the triangle and other…
Recent work [M. J. Gullans et al., Physical Review X, 11(3):031066 (2021)] has shown that quantum error correcting codes defined by random Clifford encoding circuits can achieve a non-zero encoding rate in correcting errors even if the…
We introduce the new concept of computation coding. Similar to how rate-distortion theory is concerned with the lossy compression of data, computation coding deals with the lossy computation of functions. Particularizing to linear…
Cylindrical Algebraic Decomposition (CAD) has long been one of the most important algorithms within Symbolic Computation, as a tool to perform quantifier elimination in first order logic over the reals. More recently it is finding…
A polynomial Turing compression (PTC) for a parameterized problem $L$ is a polynomial time Turing machine that has access to an oracle for a problem $L'$ such that a polynomial in the input parameter bounds each query. Meanwhile, a…
Subspace clustering refers to the task of finding a multi-subspace representation that best fits a collection of points taken from a high-dimensional space. This paper introduces an algorithm inspired by sparse subspace clustering (SSC) [In…
This paper studies the class of logarithmically completely monotonic (LCM) functions. These functions play an important role in characterising externally positive linear systems which find applications in important control problems such as…
Quantum computing promises to revolutionize various fields, yet the execution of quantum programs necessitates an effective compilation process. This involves strategically mapping quantum circuits onto the physical qubits of a quantum…
Probabilistic Circuits (PCs) are a general framework for tractable deep generative models, which support exact and efficient probabilistic inference on their learned distributions. Recent modeling and training advancements have enabled…
We introduce generalized spatially coupled parallel concatenated codes (GSC-PCCs), a class of spatially coupled turbo-like codes obtained by coupling parallel concatenated codes (PCCs) with a fraction of information bits repeated before the…
Models of computations over the integers are equivalent from a computability and complexity theory point of view by the Church-Turing thesis. It is not possible to unify discrete-time models over the reals. The situation is unclear but…
In 1990 Subramanian defined the complexity class CC as the set of problems log-space reducible to the comparator circuit value problem (CCV). He and Mayr showed that NL \subseteq CC \subseteq P, and proved that in addition to CCV several…
Clique tree conversion solves large-scale semidefinite programs by splitting an $n\times n$ matrix variable into up to $n$ smaller matrix variables, each representing a principal submatrix of up to $\omega\times\omega$. Its fundamental…
We solve an open problem related to an optimal encoding of a straight line program (SLP), a canonical form of grammar compression deriving a single string deterministically. We show that an information-theoretic lower bound for representing…
In this paper, we consider the problem of efficiently representing a set $S$ of $n$ items out of a universe $U=\{0,...,u-1\}$ while supporting a number of operations on it. Let $G=g_1...g_n$ be the gap stream associated with $S$, $gap$ its…
Over the past two decades the field of computational science and engineering (CSE) has penetrated both basic and applied research in academia, industry, and laboratories to advance discovery, optimize systems, support decision-makers, and…