Related papers: Inverse monoids associated with the complexity cla…
We initiate the study of the relationship between two complexity classes, BQP (Bounded-Error Quantum Polynomial-Time) and PPAD (Polynomial Parity Argument, Directed). We first give a conjecture that PPAD is contained in BQP, and show a…
We describe the structure of finite Boolean inverse monoids and apply our results to the representation theory of finite inverse semigroups. We then generalize to semisimple Boolean inverse semigroups.
Various characterizations are offered of injectivity of the canonical fundamental group homomorphism for a certain class of inverse limit spaces. One application characterizes the existence of a kind of generalized universal cover.
We examine possibility to design an efficient solving algorithm for problems of the class \np. It is introduced a classification of \np problems by the property that a partial solution of size $k$ can be extended into a partial solution of…
In this paper, we propose and study several inverse problems of determining unknown parameters in nonlocal nonlinear coupled PDE systems, including the potentials, nonlinear interaction functions and time-fractional orders. In these coupled…
We investigate gcd-monoids, which are cancellative monoids in which any two elements admit a left and a right gcd, and the associated reduction of multifractions (arXiv:1606.08991 and 1606.08995), a general approach to the word problem for…
The aim of this paper is to see at what extent homological properties of an inverse monoid are determined from those of its maximum group image. We provide several evidences that the maximum group image contains vital homological…
We introduce a notion of complexity of diagrams (and in particular of objects and morphisms) in an arbitrary category, as well as a notion of complexity of functors between categories equipped with complexity functions. We discuss several…
Complex functions have multiple uses in various fields of study, so analyze their characteristics it is of extensive interest to other sciences. This work begins with a particular class of rational functions of a complex variable; over this…
We introduce the inverse monoid of inner partial automorphisms of a semigroup -- a tool that associates to every semigroup an inverse semigroup. When the semigroup is a group, this inverse semigroup is isomorphic to the group of inner…
This paper is a continuation of our 2005 paper on complex topology and its implication on invertibility (or non-invertibility). In this paper, we will try to classify the complexity of inversion into 3 different classes. We will use…
Monoids generated by elements of order two appear in numerous places in the literature. For example, Coxeter reflection groups in geometry, Kuratowski monoids in topology, various monoids generated by regular operations in language theory…
The objective of this article is to formalize the definition of NP problems. We construct a mathematical model of discrete problems as independence systems with weighted elements. We introduce two auxiliary sets that characterize the…
We prove (using grammars) that the free inverse monoid of every finite rank has co-context-free word problem. Equivalently, the co-word problem of the free inverse monoid of every finite rank is context-free.
We prove an inverse relation and a family of convolution formulas involving partial Bell polynomials. Known and some presumably new combinatorial identities of convolution type are discussed. Our approach relies on an interesting…
This paper introduces and studies the higher-order group inverse in a ring. We extend known properties of the higher-order group inverse from complex matrices to elements of a ring and, in the process, derive new results. We further…
Some properties and relations satisfied by the polynomial solutions of the bispectral problem are studied. Given a differential operator, under certain restrictions its polynomial eigenfunctions are explicitly obtained, as well as the…
Reducing the NP-problems to the convex/linear analysis on the Birkhoff polytope.
The relationship between the complexity classes P and NP is an unsolved question in the field of theoretical computer science. In this paper, we look at the link between the P - NP question and the "Deterministic" versus "Non Deterministic"…
Computational complexity is examined using the principle of increasing entropy. To consider computation as a physical process from an initial instance to the final acceptance is motivated because many natural processes have been recognized…