###
*BASIC* *DEFINITIONS*

"... eshghisharifedu Abstract It is shown that the quadratic graph Q k con sisting of cycles of length k has an valuation a stronger form of the graceful valuation for every positive integer k Fur thermore additional results are obtained from the main theorem of this paper ..."

Abstract
- Add to MetaCart

eshghisharifedu Abstract It is shown that the quadratic graph Q k con sisting of cycles of length k has an valuation a stronger form of the graceful valuation for every positive integer k Fur thermore additional results are obtained from the main theorem of this paper

###
*Basics* *Definitions*

"... Abstract. Today Finite Automata are used in several areas of economy and research, for example in language and text processing or E-Commerce. There are often automata with more than hundred thousand states. Minimization of such automata can only be done by classical minimization methods. But this do ..."

Abstract
- Add to MetaCart

Abstract. Today Finite Automata are used in several areas of economy and research, for example in language and text processing or E-Commerce. There are often automata with more than hundred thousand states. Minimization of such automata can only be done by classical minimization methods. But this doesn’t produce Minimal Finite Automata with output. A Transducer is a special Finite Automata that produces an output. One of the challenges is to test the equivalence of Transducers, this will be shown in this paper.

###
*Basic* *definitions* *Definition*

, 2006

"... A topological space X is a Polish space if it is separable and ..."

###
I. *BASIC* *DEFINITIONS* AND INTERPRETATIONS

"... Abstract — The extended versions of common Laplace and Fourier transforms are given. This is achieved by defining a new function fe(p), p 2 C related to the function to be transformed f (t), t 2 R. Then fe(p) is transformed by an integral whose path is defined on an inclined line on the complex plan ..."

Abstract
- Add to MetaCart

plane. The slope of the path is the parameter of the extended

*definitions*which reduce to common transforms with zero slope. Inverse transforms of the extended versions are also defined. These proposed*definitions*, when applied to filtering in complex ordered fractional Fourier stages, significantly###
◮ *Basic* *Definitions* ◮ Classical Motivations

"... ◮ P=polynomial time. Those languages L for which there is an algorithm deciding x ∈ L in time O(|x | c) some fixed c. ◮ E.g. 2-colouring of graphs. ◮ NP=nondeterministic polynomial time. Those languages L for which there is a nondeterministic (guess and check) algorithm deciding x ∈ L in time O(|x | ..."

Abstract
- Add to MetaCart

◮ P=polynomial time. Those languages L for which there is an algorithm deciding x ∈ L in time O(|x | c) some fixed c. ◮ E.g. 2-colouring of graphs. ◮ NP=nondeterministic polynomial time. Those languages L for which there is a nondeterministic (guess and check) algorithm deciding x ∈ L in time O(|x | c) some fixed c. ◮ E.g. 3-colouring of graphs. WHERE DOES PARAMETERIZED COMPLEXITY COME FROM? ◮ A mathematical idealization is to identify “Feasible ” with P. (I won’t even bother looking at the problems with this.) ◮ With this assumption, the theory of NP-hardness is an excellent vehicle for mapping an outer boundary of intractability, for all practical purposes. ◮ Indeed, assuming the reasonable current working assumption that NTM acceptance is Ω(2 n), NP-hardness allows for practical lower bound for exact solution for problems. ◮ A very difficult practical and theoretical problem is “How can we deal with P?”. ◮ More importantly how can we deal with P − FEASIBLE, and map a further boundary of intractability. ◮ Lower bounds in P are really hard to come by. But this theory will allow you establish infeasibility for problems in P, under a reasonable complexity hypothesis. ◮ Also it will indicate to you how to attack the problem if it looks bad. ◮ It is thus both a positive and negative tool kit. I’M DUBIOUS; EXAMPLE? ◮ Below is one application that points at why the completeness theory might interest you. ◮ The great PCP Theorem of Arora et. al. allows us to show that things don’t have PTAS’s on the assumption that P=NP. ◮ Some things actually do have PTAS’s. Lets look at a couple taken from recent major conferences: STOC,

###
1.1. *Basic* *definitions*.

, 2007

"... topics and examples of quasigroups. The following lectures then introduce the three main branches of quasigroup representation theory: characters, permutation representations, and modules. 1. Quasigroups ..."

Abstract
- Add to MetaCart

topics and examples of quasigroups. The following lectures then introduce the three main branches of quasigroup representation theory: characters, permutation representations, and modules. 1. Quasigroups

###
1.1 *Basic* *definitions*

"... On the geometry and the deformation of shape represented by a piecewise continuous Bézier ..."

Abstract
- Add to MetaCart

On the geometry and the deformation of shape represented by a piecewise continuous Bézier