Related papers: Computational Complexity of Determining the Assemb…
This paper studies the computational complexity of disambiguation under probabilistic tree-grammars and context-free grammars. It presents a proof that the following problems are NP-hard: computing the Most Probable Parse (MPP) from a…
In resolving instances of a computational problem, if multiple instances of interest share a feature in common, it may be fruitful to compile this feature into a format that allows for more efficient resolution, even if the compilation is…
It is well known that selecting a good Mixed Integer Programming (MIP) formulation is crucial for an effective solution with state-of-the art solvers. While best practices and guidelines for constructing good formulations abound, there is…
Several algorithms have been proposed to compute partitions of networks into communities that score high on a graph clustering index called modularity. While publications on these algorithms typically contain experimental evaluations to…
Self-assembly is a fundamental process by which supramolecular species form spontaneously from their components. This process is ubiquitous throughout the life chemistry and is central to biological information processing. Algorithms for…
Composite minimization involves a collection of smooth functions which are aggregated in a nonsmooth manner. In the convex setting, we design an algorithm by linearizing each smooth component in accordance with its main curvature. The…
This paper deals with the computational complexity of conditions which guarantee that the NP-hard problem of finding the sparsest solution to an underdetermined linear system can be solved by efficient algorithms. In the literature, several…
We examine the computational complexity of testing and finding small plans in probabilistic planning domains with both flat and propositional representations. The complexity of plan evaluation and existence varies with the plan type sought;…
We show that the decision problem for the basic system of interpretability logic IL is PSPACE-complete. For this purpose we present an algorithm which uses polynomial space with respect to the complexity of a given formula. The existence of…
This paper proves that arrangement of music is NP-hard when subject to various constraints: avoiding musical dissonance, limiting how many notes can be played simultaneously, and limiting transition speed between chords. These results imply…
Given a countable set X (usually taken to be N or Z), an infinite permutation $\pi$ of X is a linear ordering $<_\pi$ of X. This paper investigates the combinatorial complexity of infinite permutations on N associated with the image of…
Determining the complexity of molecules has important applications from molecular design to understanding the history of the process that led to the formation of the molecule. Currently, it is not possible to experimentally determine,…
We review some recent results related to the self-assembly of infinite structures in the Tile Assembly Model. These results include impossibility results, as well as novel tile assembly systems in which shapes and patterns that represent…
We use computer simulations to investigate self-assembly in a system of model chaperonin proteins, and in an Ising lattice gas. We discuss the mechanisms responsible for rapid and efficient assembly in these systems, and we use measurements…
We investigate the complexity of the separation problem associated to classes of regular languages. For a class C, C-separation takes two regular languages as input and asks whether there exists a third language in C which includes the…
In a previous paper, an implementable algorithm was introduced to compute discrete solutions of sweeping processes (i.e. specific first order differential inclusions). The convergence of this numerical scheme was proved thanks to…
Post Embedding Problems are a family of decision problems based on the interaction of a rational relation with the subword embedding ordering, and are used in the literature to prove non multiply-recursive complexity lower bounds. We refine…
Although there is a somewhat standard formalization of computability on countable sets given by Turing machines, the same cannot be said about uncountable sets. Among the approaches to define computability in these sets, order-theoretic…
In the well-known complexity class NP are combinatorial problems, whose optimization counterparts are important for many practical settings. These problems typically consider full knowledge about the input. In practical settings, however,…
Consider a fixed universe of $N=2^n$ elements and the uniform distribution over elements of some subset of size $K$. Given samples from this distribution, the task of complement sampling is to provide a sample from the complementary subset.…