Guillermo Morales-Luna Theory of Algorithms – Course Handouts –

Guillermo Morales - Luna Theory of Algorithms – Course Handouts – November 30 , 2009 Cinvestav - IPN

We introduce here the most basic concepts in measuring algorithms complexities. Initially we distinguish behaviors according to the computational costs due to their inputs. Then we introduce some mathematical functions of extended use in measuring algorithmic performances, and the growth orders of maps. We study the sums, with either finite or countable number of summands, and the convergence p...

A Propositional Calculus for Threshold Logic

On Formal Expressions of BRW-polynomials

Algebraic expressions of the Bernstein-Rabin-Winograd-polynomials, when defined over the field of the rational numbers, are obtained by recursion.

Approximation Algorithms for Maxsat

The main aim of NP-completeness theory is the analysis of intractabil-ity. Many optimization problems were rst proved to be NP-hard. Since the complete solution of these problems requires exponential time, polynomial time algorithms to nd \near-optimal" solutions, i.e., approximation algorithms, appear to be viable. In this paper we show the basic principles of Approximation Theory for NP-compl...

A Geometric Presentation of Probabilistic Satisfiability

By considering probability distributions over the set of assignments the expected truth values assignment to propositional variables are extended through linear operators, and the expected truth values of the clauses at any given conjunctive form are also extended through linear maps. The probabilistic satisfiability problems are discussed in terms of the introduced linear extensions. The case ...