scholarly journals Ramsey Theory Applications

10.37236/34 ◽  
2004 ◽  
Vol 1000 ◽  
Author(s):  
Vera Rosta
Keyword(s):  
Information Theory ◽  
Number Theory ◽  
Computer Science ◽  
Ergodic Theory ◽  
Set Theory ◽  
Ramsey Theory ◽  
Theoretical Computer Science ◽  
Theoretical Computer ◽  
Ramsey Type

There are many interesting applications of Ramsey theory, these include results in number theory, algebra, geometry, topology, set theory, logic, ergodic theory, information theory and theoretical computer science. Relations of Ramsey-type theorems to various fields in mathematics are well documented in published books and monographs. The main objective of this survey is to list applications mostly in theoretical computer science of the last two decades not contained in these.

Relations in the semigroup of 2 × 2 upper-triangular matrices

2020 ◽  
Vol 30 (03) ◽  
pp. 567-584
Author(s):  
Henri-Alex Esbelin ◽  
Marin Gutan
Keyword(s):  
Number Theory ◽  
Computer Science ◽  
Semigroup Theory ◽  
Theoretical Computer Science ◽  
Multiplicative Semigroup ◽  
Triangular Matrices ◽  
Theoretical Computer ◽  
Upper Triangular Matrices ◽  
Matrix Semigroups

Let [Formula: see text] with [Formula: see text] be [Formula: see text] upper-triangular matrices with rational entries. In the multiplicative semigroup generated by these matrices, we check if there are relations of the form [Formula: see text] where [Formula: see text] [Formula: see text] and [Formula: see text] We give algorithms to find relations of the previous form. Our results are extensions of some theorems obtained by Charlier and Honkala in [The freeness problem over matrix semigroups and bounded languages, Inf. Comput. 237 (2014) 243–256]. Our paper is at the interface between algebra, number theory and theoretical computer science. While the main results concern decidability and semigroup theory, the methods for obtaining them come from number theory.

An Essay on Denotational Mathematics

2019 ◽  
pp. 1629-1640
Author(s):  
Giuseppe Iurato
Keyword(s):  
Artificial Intelligence ◽  
Computer Science ◽  
Set Theory ◽  
Neuronal Networks ◽  
Theoretical Computer Science ◽  
Mathematical Framework ◽  
Theoretical Computer ◽  
Cognitive Informatics ◽  
Naive Set Theory ◽  
Software Science

Denotational mathematics is a new rigorous discipline of theoretical computer science that springs out from the attempt to provide a suitable mathematical framework in which laid out new algebraic structures formalizing certain formal patterns coming from computational and natural intelligence, software science, cognitive informatics, neuronal networks, and artificial intelligence. In this chapter, a very brief but rigorous exposition of the main formal structures of denotational mathematics is outlined within naive set theory.

An Essay on Denotational Mathematics

2018 ◽  
pp. 7704-7714 ◽  
Author(s):  
Giuseppe Iurato
Keyword(s):  
Artificial Intelligence ◽  
Computer Science ◽  
Set Theory ◽  
Neuronal Networks ◽  
Theoretical Computer Science ◽  
Mathematical Framework ◽  
Theoretical Computer ◽  
Cognitive Informatics ◽  
Naive Set Theory ◽  
Software Science

Denotational mathematics is a new rigorous discipline of theoretical computer science which springs out from the attempt to provide a suitable mathematical framework in which laid out new algebraic structures formalizing certain formal patterns coming from computational and natural intelligence, software science, cognitive informatics, neuronal networks, artificial intelligence. In this chapter, a very brief but rigorous exposition of the main formal structures of denotational mathematics, is outlined within naive set theory.

Sign in / Sign up

Export Citation Format

Share Document