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This paper concerns the explicit treatment of substitutions in the lambda calculus. One of its contributions is the simplification and rationalization of the suspension calculus that embodies such a treatment. The earlier version of this…

Logic in Computer Science · Computer Science 2007-05-23 Andrew Gacek , Gopalan Nadathur

The task of inferring logical formulas from examples has garnered significant attention as a means to assist engineers in creating formal specifications used in the design, synthesis, and verification of computing systems. Among various…

Logic in Computer Science · Computer Science 2025-06-04 Benjamin Bordais , Daniel Neider

A wide range of studies in population genetics have employed the sample frequency spectrum (SFS), a summary statistic which describes the distribution of mutant alleles at a polymorphic site in a sample of DNA sequences. In particular,…

Probability · Mathematics 2016-03-03 John A. Kamm , Jonathan Terhorst , Yun S. Song

The Burrows-Wheeler Transform (BWT) serves as the basis for many important sequence indexes. On very large datasets (e.g. genomic databases), classical BWT construction algorithms are often infeasible because they usually need to have the…

Data Structures and Algorithms · Computer Science 2025-09-24 Jannik Olbrich

We show that the discrete complex, and numerous hypercomplex, Fourier transforms defined and used so far by a number of researchers can be unified into a single framework based on a matrix exponential version of Euler's formula…

Rings and Algebras · Mathematics 2012-09-13 Stephen J. Sangwine , Todd A. Ell

In 2012, Diem introduced a new figure of merit for cryptographic sequences called expansion complexity. In this paper, we slightly modify this notion to obtain the so-called irreducible-expansion complexity which is more suitable for…

Number Theory · Mathematics 2017-02-20 Gómez-Pérez , László Mérai , Harald Niederreiter

We present a method, illustrated by several examples, to find explicit counts of permutations containing a given multiset of three letter patterns. The method is recursive, depending on bijections to reduce to the case of a smaller…

Combinatorics · Mathematics 2007-05-23 David Callan

Permutation tests are among the simplest and most widely used statistical tools. Their p-values can be computed by a straightforward sampling of permutations. However, this way of computing p-values is often so slow that it is replaced by…

Computation · Statistics 2018-07-27 Jean-Marie Droz

We study optimization problems that are neither approximable in polynomial time (at least with a constant factor) nor fixed parameter tractable, under widely believed complexity assumptions. Specifically, we focus on Maximum Independent…

Data Structures and Algorithms · Computer Science 2008-10-29 Marek Cygan , Lukasz Kowalik , Marcin Pilipczuk , Mateusz Wykurz

The unstructured sparsity after pruning poses a challenge to the efficient implementation of deep learning models in existing regular architectures like systolic arrays. On the other hand, coarse-grained structured pruning is suitable for…

Machine Learning · Computer Science 2024-11-22 Xizi Chen , Jingyang Zhu , Jingbo Jiang , Chi-Ying Tsui

This paper introduces an algebraic combinatorial approach to simplicial cone decompositions, a key step in solving inhomogeneous linear Diophantine systems and counting lattice points in polytopes. We use constant term manipulation on the…

Combinatorics · Mathematics 2025-01-14 Guoce Xin , Xinyu Xu , Zihao Zhang

In [4] we describe a variation of the classical permutation decoding algorithm that can be applied to any binary affine-invariant code; in particular, it can be applied to first-order Reed-Muller codes successfully. In this paper we study…

Information Theory · Computer Science 2025-09-16 José Joaquín Bernal , Juan Jacobo Simón

We introduce a new framework for the analysis of preprocessing routines for parameterized counting problems. Existing frameworks that encapsulate parameterized counting problems permit the usage of exponential (rather than polynomial) time…

Data Structures and Algorithms · Computer Science 2023-08-07 Daniel Lokshtanov , Pranabendu Misra , Saket Saurabh , Meirav Zehavi

We live in a period where bio-informatics is rapidly expanding, a significant quantity of genomic data has been produced as a result of the advancement of high-throughput genome sequencing technology, raising concerns about the costs…

Quantitative Methods · Quantitative Biology 2023-03-10 Mehedi Hasan Sarkar , Adnan Ferdous Ashrafi

In this paper we show that every combinatorial problem has an exact explicit equation that returns its solution. We present a method to obtain an equation that solves exactly any combinatorial problem, both inversion, constraint…

Emerging Technologies · Computer Science 2025-02-11 Alejandro Mata Ali

At the core of any inference procedure in deep neural networks are dot product operations, which are the component that require the highest computational resources. A common approach to reduce the cost of inference is to reduce its memory…

Machine Learning · Computer Science 2018-12-19 Simon Wiedemann , Klaus-Robert Müller , Wojciech Samek

Submodular function minimization (SFM) is a fundamental and efficiently solvable problem class in combinatorial optimization with a multitude of applications in various fields. Surprisingly, there is only very little known about constraint…

Data Structures and Algorithms · Computer Science 2018-11-27 Martin Nägele , Benny Sudakov , Rico Zenklusen

Kernelization algorithms in the context of Parameterized Complexity are often based on a combination of reduction rules and combinatorial insights. We will expose in this paper a similar strategy for obtaining polynomial-time approximation…

Data Structures and Algorithms · Computer Science 2014-09-15 Faisal N. Abu-Khzam , Cristina Bazgan , Morgan Chopin , Henning Fernau

In this article, we provide a new algorithm for solving constraint satisfaction problems over templates with few subpowers, by reducing the problem to the combination of solvability of a polynomial number of systems of linear equations over…

Logic · Mathematics 2017-11-07 Dejan Delic , Amir El-Aooiti

We study the expansions of permutation statistics in the basis of functions counting occurrences of a fixed pattern in a permutation. We show the finiteness of these pattern expansions for a class of permutation statistics including the…

Combinatorics · Mathematics 2026-01-08 Ian Cavey , Hugh Dennin , Bridget Eileen Tenner