Related papers: Philosophical Solution to P=?NP: P is Equal to NP
We address two sets of long-standing open questions in probability theory, from a computational complexity perspective: divisibility of stochastic maps, and divisibility and decomposability of probability distributions. We prove that finite…
Probabilistic circuits (PCs) such as sum-product networks efficiently represent large multi-variate probability distributions. They are preferred in practice over other probabilistic representations such as Bayesian and Markov networks…
We present a new algorithm for exactly solving decision making problems represented as influence diagrams. We do not require the usual assumptions of no forgetting and regularity; this allows us to solve problems with simultaneous decisions…
The increasing amount of data processed on edge and the demand for reducing the energy consumption for large neural network architectures have initiated the transition from traditional von Neumann architectures towards in-memory computing…
If quantum states exhibit small nonlinearities during time evolution, then quantum computers can be used to solve NP-complete problems in polynomial time. We provide algorithms that solve NP-complete and #P oracle problems by exploiting…
Neural Turing Machines (NTM) contain memory component that simulates "working memory" in the brain to store and retrieve information to ease simple algorithms learning. So far, only linearly organized memory is proposed, and during…
The existence of a (p-)optimal propositional proof system is a major open question in (proof) complexity; many people conjecture that such systems do not exist. Krajicek and Pudlak (1989) show that this question is equivalent to the…
We introduce the NP-complete problem 3SAT_N and extend Tovey's results to a classification theorem for this problem. This theorem leads us to generalize the concept of truth assignments for SAT to aggressive truth assignments for 3SAT_N. We…
We survey recent developments in the study of probabilistic complexity classes. While the evidence seems to support the conjecture that probabilism can be deterministically simulated with relatively low overhead, i.e., that $P=BPP$, it also…
We consider a monopolist seller facing a single buyer with additive valuations over n heterogeneous, independent items. It is known that in this important setting optimal mechanisms may require randomization [HR12], use menus of infinite…
We present an original model of paraconsistent Turing machines (PTMs), a generalization of the classical Turing machines model of computation using a paraconsistent logic. Next, we briefl y describe the standard models of quantum…
We consider the parity variants of basic problems studied in fine-grained complexity. We show that finding the exact solution is just as hard as finding its parity (i.e. if the solution is even or odd) for a large number of classical…
We approach the 3-SAT satisfiability problem with the quantum-inspired method of imaginary time propagation (ITP) applied to matrix product states (MPS) on a classical computer. This ansatz is fundamentally limited by a quantum entanglement…
A novel neural network (NN) approach is proposed for constrained optimization. The proposed method uses a specially designed NN architecture and training/optimization procedure called Neural Optimization Machine (NOM). The objective…
The aim of this thesis is to determine classes of NP relations for which random generation and approximate counting problems admit an efficient solution. Since efficient rank implies efficient random generation, we first investigate some…
This paper introduces and studies a new model of computation called an Alternating Automatic Register Machine (AARM). An AARM possesses the basic features of a conventional register machine and an alternating Turing machine, but can carry…
Advancements in mathematical programming have made it possible to efficiently tackle large-scale real-world problems that were deemed intractable just a few decades ago. However, provably optimal solutions may not be accepted due to the…
We consider the Demand Strip Packing problem (DSP), in which we are given a set of jobs, each specified by a processing time and a demand. The task is to schedule all jobs such that they are finished before some deadline $D$ while…
Processing-in-Memory (PIM) has emerged as a promising computing paradigm to address the memory wall and the fundamental bottleneck of the von Neumann architecture by reducing costly data movement between memory and processing units. As with…
Parameterization and approximation are two popular ways of coping with NP-hard problems. More recently, the two have also been combined to derive many interesting results. We survey developments in the area both from the algorithmic and…