Related papers: NP-completeness of Certain Sub-classes of the Synd…
Graph packing and partitioning problems have been studied in many contexts, including from the algorithmic complexity perspective. Consider the packing problem of determining whether a graph contains a spanning tree and a cycle that do not…
Syndrome decoding is an integral but computationally demanding step in the implementation of quantum error correction for fault-tolerant quantum computing. Here, we report the development and benchmarking of Artificial Neural Network (ANN)…
Recently, due to the genomic sequence analysis in several types of cancer, the genomic data based on {\em copy number profiles} ({\em CNP} for short) are getting more and more popular. A CNP is a vector where each component is a…
NP-Complete problems have an important attribute that if one NP-Complete problem can be solved in polynomial time, all NP-Complete problems will have a polynomial solution. The 3-CNF-SAT problem is a NP-Complete problem and the primary…
The problem of when a given digraph contains a subdivision of a fixed digraph $F$ is considered. Bang-Jensen et al. laid out foundations for approaching this problem from the algorithmic point of view. In this paper we give further support…
The hairpin completion is an operation on formal languages which is inspired by the hairpin formation in biochemistry. Hairpin formations occur naturally within DNA-computing. It has been known that the hairpin completion of a regular…
A non-binary Constraint Satisfaction Problem (CSP) can be solved directly using extended versions of binary techniques. Alternatively, the non-binary problem can be translated into an equivalent binary one. In this case, it is generally…
Here we study the computational complexity of the constrained synchronization problem for the class of regular commutative constraint languages. Utilizing a vector representation of regular commutative constraint languages, we give a full…
Recent studies have revealed a number of pathologies of neural machine translation (NMT) systems. Hypotheses explaining these mostly suggest there is something fundamentally wrong with NMT as a model or its training algorithm, maximum…
Despite strong performance on a variety of tasks, neural sequence models trained with maximum likelihood have been shown to exhibit issues such as length bias and degenerate repetition. We study the related issue of receiving…
In a spiking neural network (SNN), individual neurons operate autonomously and only communicate with other neurons sparingly and asynchronously via spike signals. These characteristics render a massively parallel hardware implementation of…
In this paper, we prove that the numerical-semigroup-gap counting problem is #NP-complete as a main theorem. A numerical semigroup is an additive semigroup over the set of all nonnegative integers. A gap of a numerical semigroup is defined…
Testing if a given graph $G$ contains the $k$-vertex path $P_k$ as a minor or as an induced minor is trivial for every fixed integer $k\geq 1$. However, the situation changes for the problem of checking if a graph can be modified into $P_k$…
The NP-hard general factor problem asks, given a graph and for each vertex a list of integers, whether the graph has a spanning subgraph where each vertex has a degree that belongs to its assigned list. The problem remains NP-hard even if…
We show that the following problems are NP-complete. 1. Can the vertex set of a graph be partitioned into two sets such that each set induces a perfect graph? 2. Is the difference between the chromatic number and clique number at most $1$…
In this paper, we propose a subgradient algorithm with a non-asymptotic convergence guarantee to solve copositive programming problems. The subproblem to be solved at each iteration is a standard quadratic programming problem, which is…
Using well-known mathematical problems for encryption is a widely used technique because they are computationally hard and provide security against potential attacks on the encryption method. The subset sum problem (SSP) can be defined as…
A computational secret-sharing scheme is a method that enables a dealer, that has a secret, to distribute this secret among a set of parties such that a "qualified" subset of parties can efficiently reconstruct the secret while any…
The notion of graph covers (also referred to as locally bijective homomorphisms) plays an important role in topological graph theory and has found its computer science applications in models of local computation. For a fixed target graph…
In this work, we introduce a novel variant of the multivariate quadratic problem, which is at the core of one of the most promising post-quantum alternatives: multivariate cryptography. In this variant, the solution of a given multivariate…