Related papers: On the relationship between classes P and NP
The method for analyzing algorithmic runtime complexity using decision trees is discussed using the sorting algorithm. This method is then extended to optimal algorithms which may find all cliques of size q in network N, or simply the first…
The open question, P=NP?, was presented by Cook (1971). In this paper, a proof that P is not equal to NP is presented. In addition, it is shown that P is not equal to the intersection of NP and co-NP. Finally, the exact inclusion…
The P=?NP problem is philosophically solved by showing P is equal to NP in the random access with unit multiply (MRAM) model. It is shown that the MRAM model empirically best models computation hardness. The P=?NP problem is shown to be a…
$P \overset{\text{?}}{=} NP$ or $P\ vs\ NP$ is the core problem in computational complexity theory. In this paper, we proposed a definition of linear correlation of derived matrix and system, and discussed the linear correlation of $P$ and…
This paper considers the question of P = NP in context of the polynomial time SAT algorithm. It posits proposition dependent on existence of conjectured problem that even where the algorithm is shown to solve SAT in polynomial time it…
An important objective of research in counting complexity is to understand which counting problems are approximable. In this quest, the complexity class TotP, a hard subclass of #P, is of key importance, as it contains self-reducible…
Though many ontologies have huge number of classes, one cannot find a good number of object properties connecting the classes in most of the cases. Adding object properties makes an ontology richer and more applicable for tasks such as…
We consider the relationship between learnability of a "base class" of functions on a set $X$, and learnability of a class of statistical functions derived from the base class. For example, we refine results showing that learnability of a…
About 25 years ago, it came to light that a single combinatorial property determines both an important dividing line in model theory (NIP) and machine learning (PAC-learnability). The following years saw a fruitful exchange of ideas between…
In an era where learning is considered a problem, we decided to go for problems for the sake of learning! The purpose of this study was to throw light on the issues involved in two forms of PBL viz., Case Study Based PBL and Research Based…
Hybrid Probabilistic Programs (HPPs) are logic programs that allow the programmer to explicitly encode his knowledge of the dependencies between events being described in the program. In this paper, we classify HPPs into three classes…
Isomorphisms p between pattern classes A and B are considered. It is shown that, if p is not a symmetry of the entire set of permutations, then, to within symmetry, A is a subset of one a small set of pattern classes whose structure,…
Link prediction (LP) is an important problem in network science and machine learning research. The state-of-the-art LP methods are usually evaluated in a uniform setup, ignoring several factors associated with the data and application…
Analogy has been shown to be important in many key cognitive abilities, including learning, problem solving, creativity and language change. For cognitive models of analogy, the fundamental computational question is how its inherent…
Problem-based learning (PBL) is a constructivist learner-centered instructional approach based on the analysis, resolution and discussion of a given problem. It can be applied to any subject, indeed it is especially useful for the teaching…
People usually regard algorithms as more abstract than the programs that implement them. The natural way to formalize this idea is that algorithms are equivalence classes of programs with respect to a suitable equivalence relation. We argue…
What makes a task relatively more or less difficult for a machine compared to a human? Much AI/ML research has focused on expanding the range of tasks that machines can do, with a focus on whether machines can beat humans. Allowing for…
The question of whether the complexity class P is equal to the complexity class NP has been a seemingly intractable problem for over 4 decades. It has been clear that if an algorithm existed that would solve the problems in the NP class in…
This extended abstract presents an overview on NP-hard optimization problems with multiple interdependent components. These problems occur in many real-world applications: industrial applications, engineering, and logistics. The fact that…
Optimization problems are ubiquitous in our societies and are present in almost every segment of the economy. Most of these optimization problems are NP-hard and computationally demanding, often requiring approximate solutions for…