Related papers: A Multivariate Complexity Analysis of Qualitative …
Quantum computers have the potential to efficiently solve a system of nonlinear ordinary differential equations (ODEs), which play a crucial role in various industries and scientific fields. However, it remains unclear which system of…
Many problems in static program analysis can be modeled as the context-free language (CFL) reachability problem on directed labeled graphs. The CFL reachability problem can be generally solved in time $O(n^3)$, where $n$ is the number of…
In this paper we identify certain peculiar systems of 2 discrete-time evolution equations,x~n = F^(n)(x1; x2) , n = 1, 2 , which are algebraically solvable. Here l is the "discrete-time" independent variable taking integer values (l = 0, 1,…
Temporal Equilibrium Logic (TEL) is a promising framework that extends the knowledge representation and reasoning capabilities of Answer Set Programming with temporal operators in the style of LTL. To our knowledge it is the first…
We study the binary perceptron, a random constraint satisfaction problem that asks to find a Boolean vector in the intersection of independently chosen random halfspaces. A striking feature of this model is that at every positive constraint…
In logic-based knowledge representation, query answering has essentially replaced mere satisfiability checking as the inferencing problem of primary interest. For knowledge bases in the basic description logic ALC, the computational…
In this paper, we show new algorithms, hardness results and applications for $\sf{S|LWE\rangle}$ and $\sf{C|LWE\rangle}$ with real Gaussian, Gaussian with linear or quadratic phase terms, and other related amplitudes. Let $n$ be the…
An important aspect of artificial intelligence (AI) is the ability to reason in a step-by-step "algorithmic" manner that can be inspected and verified for its correctness. This is especially important in the domain of question answering…
The Problem of Time is that `time' in each of ordinary quantum theory and general relativity are mutually incompatible notions. This causes difficulties in trying to put these two theories together to form a theory of Quantum Gravity. The…
A random walk-based method is proposed to efficiently compute the solution of a large class of fractional in time linear systems of differential equations (linear F-ODE systems), along with the derivatives with respect to the system…
As predictive machine learning models become increasingly adopted and advanced, their role has evolved from merely predicting outcomes to actively shaping them. This evolution has underscored the importance of Trustworthy AI, highlighting…
Complex queries for massive data analysis jobs have become increasingly commonplace. Many such queries contain com- mon subexpressions, either within a single query or among multiple queries submitted as a batch. Conventional query…
We obtain a number of lower bounds on the running time of algorithms solving problems on graphs of bounded treewidth. We prove the results under the Strong Exponential Time Hypothesis of Impagliazzo and Paturi. In particular, assuming that…
The problem of finding a nontrivial factor of a polynomial f(x) over a finite field F_q has many known efficient, but randomized, algorithms. The deterministic complexity of this problem is a famous open question even assuming the…
We present the first near optimal approximation schemes for the maximum weighted (uncapacitated or capacitated) $b$--matching problems for non-bipartite graphs that run in time (near) linear in the number of edges. For any…
Many algorithms have been developed for NP-hard problems on graphs with small treewidth $k$. For example, all problems that are expressable in linear extended monadic second order can be solved in linear time on graphs of bounded treewidth.…
Given a set of $n$ colored points $P \subset \mathbb{R}^d$ we wish to store $P$ such that, given some query region $Q$, we can efficiently report the colors of the points appearing in the query region, along with their frequencies. This is…
Neural Ordinary Differential Equations (ODEs) are elegant reinterpretations of deep networks where continuous time can replace the discrete notion of depth, ODE solvers perform forward propagation, and the adjoint method enables efficient,…
We present randomized algorithms for some well-studied, hard combinatorial problems: the k-path problem, the p-packing of q-sets problem, and the q-dimensional p-matching problem. Our algorithms solve these problems with high probability in…
In a classical scheduling problem, we are given a set of $n$ jobs of unit length along with precedence constraints, and the goal is to find a schedule of these jobs on $m$ identical machines that minimizes the makespan. Using the standard…