Related papers: Loop Patterns: Extension of Kleene Star Operator f…
Matrix Code gives imperative programming a mathematical semantics and heuristic power comparable in quality to functional and logic programming. A program in Matrix Code is developed incrementally from a specification in pre/post-condition…
Recurrence equations have played a central role in static cost analysis, where they can be viewed as abstractions of programs and used to infer resource usage information without actually running the programs with concrete data. Such…
In data storage and data transmission, certain patterns are more likely to be subject to error when written (transmitted) onto the media. In magnetic recording systems with binary data and bipolar non-return-to-zero signaling, patterns that…
CPEG is an extended parsing expression grammar with regex-like capture annotation. Two annotations (capture and left-folding) allow a flexible construction of syntax trees from arbitrary parsing patterns. More importantly, CPEG is designed…
Sparse data models, where data is assumed to be well represented as a linear combination of a few elements from a dictionary, have gained considerable attention in recent years, and their use has led to state-of-the-art results in many…
We show that polynomial codes (and some related codes) used for distributed matrix multiplication are interleaved Reed-Solomon codes and, hence, can be collaboratively decoded. We consider a fault tolerant setup where $t$ worker nodes…
We propose an extension of the framework for discussing the computational complexity of problems involving uncountably many objects, such as real numbers, sets and functions, that can be represented only through approximation. The key idea…
Numerical applications and, more recently, machine learning applications rely on high-dimensional data that is typically organized into multi-dimensional tensors. Many existing frameworks, libraries, and domain-specific languages support…
Many services today massively and continuously produce log files of different and varying formats. These logs are important since they contain information about the application activities, which is necessary for improvements by analyzing…
Automated techniques such as model checking have been used to verify models of robotic mission plans based on Markov decision processes (MDPs) and generate counterexamples that may help diagnose requirement violations. However, such…
We study the equational theory of the Weihrauch lattice with composition and iterations, meaning the collection of equations between terms built from variables, the lattice operations $\sqcup$, $\sqcap$, the composition operator $\star$ and…
In recent years, a class of dictionaries have been proposed for multidimensional (tensor) data representation that exploit the structure of tensor data by imposing a Kronecker structure on the dictionary underlying the data. In this work, a…
We redefine the transition function of elementary cellular automata (ECA) in terms of discrete operators. The operator representation provides a clear hint about the way systems behave both at the local and the global scale. We show that…
Loop percolation, also known as the dense O(1) loop model, is a variant of critical bond percolation in the square lattice Z^2 whose graph structure consists of a disjoint union of cycles. We study its connectivity pattern, which is a…
In this work, we explore Landin's Knot, which is understood as a pattern for encoding general recursion, including non-termination, that is possible after adding higher-order references to an otherwise terminating language. We observe that…
Evolutionary algorithms usually explore a search space of solutions by means of crossover and mutation. While a mutation consists of a small, local modification of a solution, crossover mixes the genetic information of two solutions to…
We propose a novel approach to iterated sparse matrix dense matrix multiplication, a fundamental computational kernel in scientific computing and graph neural network training. In cases where matrix sizes exceed the memory of a single…
We investigate the nondeterministic state complexity of basic operations for suffix-free regular languages. The nondeterministic state complexity of an operation is the number of states that are necessary and sufficient in the worst-case…
Sparse modeling is a powerful framework for data analysis and processing. Traditionally, encoding in this framework is done by solving an l_1-regularized linear regression problem, usually called Lasso. In this work we first combine the…
Kleene algebra with tests is an extension of Kleene algebra, the algebra of regular expressions, which can be used to reason about programs. We develop a coalgebraic theory of Kleene algebra with tests, along the lines of the coalgebraic…