Related papers: A Measure of Space for Computing over the Reals
It is known that the satisfiability problems of the product logics K4xS5 and S4xS5 are NEXPTIME-hard and that the satisfiability problem of the logic SSL of subset spaces is PSPACE-hard. We improve these lower bounds for the complexity of…
The demand for extracting rules from high dimensional real world data is increasing in various fields. However, the possible redundancy of such data sometimes makes it difficult to obtain a good generalization ability for novel samples. To…
We show that the problem of determining the feasibility of quadratic systems over $\mathbb{C}$, $\mathbb{R}$, and $\mathbb{Z}$ requires exponential time. This separates P and NP over these fields/rings in the BCSS model of computation.
In this paper, we investigate computational power of threshold circuits and other theoretical models of neural networks in terms of the following four complexity measures: size (the number of gates), depth, weight and energy. Here the…
We introduce a novel variant of BSS machines called Separate Branching BSS machines (S-BSS in short) and develop a Fagin-type logical characterisation for languages decidable in non-deterministic polynomial time by S-BSS machines. We show…
Planarity Testing is the problem of determining whether a given graph is planar while planar embedding is the corresponding construction problem. The bounded space complexity of these problems has been determined to be exactly Logspace by…
In an influential paper, Levesque proposed a formal specification for analysing the correctness of program-like plans, such as conditional plans, iterative plans, and knowledge-based plans. He motivated a logical characterisation within the…
We show that if the probabilistic logarithmic-space solver or the deterministic nearly logarithmic-space solver for undirected Laplacian matrices can be extended to solve slightly larger subclasses of linear systems, then they can be use to…
In process mining, alignments quantify the degree of deviation between an observed event trace and a business process model and constitute the most important conformance checking technique. We study the algorithmic complexity of computing…
In this paper we study the fine-grained complexity of finding exact and approximate solutions to problems in P. Our main contribution is showing reductions from exact to approximate solution for a host of such problems. As one (notable)…
We explain how the popular, highly abstract MapReduce model of parallel computation (MRC) can be rooted in reality by explaining how it can be simulated on realistic distributed-memory parallel machine models like BSP. We first refine the…
Circuit complexity has been used as a tool to study various properties in condensed matter systems, in particular as a way to probe the phase diagram. However, compared with measures based on entanglement, complexity has been found lacking.…
We study the verification of distributed systems where processes are finite automata with access to a shared pool of locks. We consider objectives that are boolean combinations of local regular constraints. We show that the problem,…
A celebrated theorem of Savitch states that NSPACE(S) is contained in DSPACE(S^2). In particular, Savitch gave a deterministic algorithm to solve ST-CONNECTIVITY (an NL-complete problem) using O(log^2{n}) space, implying NL is in…
"Sparse" neural networks, in which relatively few neurons or connections are active, are common in both machine learning and neuroscience. Whereas in machine learning, "sparsity" is related to a penalty term that leads to some connecting…
We show how perceptual embeddings of the visual system can be constructed at inference-time with no training data or deep neural network features. Our perceptual embeddings are solutions to a weighted least squares (WLS) problem, defined at…
A constraint satisfaction problem (CSP) is a computational problem where the input consists of a finite set of variables and a finite set of constraints, and where the task is to decide whether there exists a satisfying assignment of values…
A significant progress has been made in the past three decades over the study of combinatorial NP optimization problems and their associated optimization and approximate classes, such as NPO, PO, APX (or APXP), and PTAS. Unfortunately, a…
Constraint satisfaction problems (CSPs) for first-order reducts of finitely bounded homogeneous structures form a large class of computational problems that might exhibit a complexity dichotomy, P versus NP-complete. A powerful method to…
In the rapidly evolving field of quantum computing, quantifying circuit complexity remains a critical challenge. This paper introduces Character Complexity, a novel measure that bridges Group-theoretic concepts with practical quantum…