COM273: Automata, Computability, and Formal Languages
REVIEW NOTES

Connected graph A graph G is connected if given any vertices u and v in G, there is a path from u to v (or v to u). That is, in a connected graph, we can get from any vertex to any other vertex on a path. If there’s no path between some pair of vertices then the graph is called disconnected. The following shows a connected graph and a disconnected graph. Example: a b c b a c

e d connected graph

e d disconnected graph

Cycle A cycle (or a circuit) is a path of non-zero length from u to v with no repeated edges. A simple cycle is cycle from v to v, in which there are no repeated vertices (except for the initial and final vertices which are both equal to v) Example: a b d e c (a, b, d, c, b, e, c, a) is a cycle (but not simple) (a, d, c, b, e, a) is a simple cycle of length 5.

Notice that a simple path of length n contains (n+1) distinct vertices, which a simple cycle of length n contains n distinct vertices.

Eulerian graphs A cycle in a connected graph G that includes all the edges and all the vertices of G is called an Euler cycle (“Euler” is pronounced as “oiler”).

A connected graph containing an Euler cycle is called an Eulerian graph.

Finding an Euler cycle in a graph is the same as playing the following “game”. Draw the entire graph without lifting your pen which drawing all the edges exactly once, and visiting all the vertices, starting from and ending at the same vertex. Example: Try playing the “game” described above to show that graphs (1) – (5)is the following graphs are Eulerian. Graph (6) is not Eulerian because you can’t draw the entire graph starting and ending with the same vertex.

(1) (2)

(3)

(4)

(5)

(6)

Special Types of Graphs There are certain types of graphs to which we give special names. 1. 2. 3. 4. 5. Trivial graph – a graph of order 1 and size 0. Null graph – a graph of order n and size 0; denoted by Nn. Cycle graph – a graph of...

...changing at a rapid pace and informality in the English language is on the rise. In places where formallanguage was once a must, informality has taken over, and questions are raised over whether formallanguage still has a place in modern English. However, despite changes, formallanguage is still in use and is still expected and considered the most appropriate method of address in many...

...Languages, Grammars, and Automata Theory
Discrete Mathematics
Linda Chalk
Colorado Technical University
Professor Timothy Manzke
December 17, 2010
Languages, grammars and automata theory are all related to computer applications. Grammar is the rule for language structure regardless of the meaning. For computer programming languages context free grammar (CFG) is commonly used. Formal...

...
Deque Automata for all classes of Formallanguages
B. Asha latha1
Department of computers
SRKIT Engineering
Vijayawada Andhra Pradesh (India)
T.Vishnupriya2
Department of Electronics
SRKIT Vijayawada, Andhra Pradesh (India)
N.Himabindu3
Department of computers
KBN College of Vijayawada, Andhra Pradesh (India)
Abstract: The purpose of computation involves solving problems by communicating them to a computational model by means of a suitable...

... 16
ESSAY
The environment necessary for the development of language can be enhanced to structure the child from birth to six years. How is language encouraged in the Montessori nursery class?
A Montessori nursery classroom is a prepared environment for children from the ages of 2 1/2 to 6 years...

...Alphabets, Strings and Languages
Example : Consider the string 011 over the binary alphabet. All the prefixes, suffixes and substrings of this string are listed below.
Prefixes: e, 0, 01, 011.
Suffixes: e, 1, 11, 011.
Substrings: e, 0, 1, 01, 11, 011.
Note that x is a prefix (suffix or substring) to x, for any string x and e is a prefix (suffix or substring) to any string.
A string x is a proper prefix (suffix) of string y if x is a prefix (suffix) of y and x y.
In the...

...Language and Identity
First of all, Identity is the belief as “who we are and how we are” which we all have as individuals and it is based on many fundamental factors such as Ethnic group,
Racial, National, Gendered, Social Class, Language, Sexual and Religious. As it is clear that identity has many essentials and it is not made of just one fact but has something to do with many, I will focus on the relationship especially between...

...Importance of language
The importance of language is essential to every aspect and interaction in our everyday lives. We use language to inform the people around us of what we feel, what we desire, and question/understand the world around us. We communicate effectively with our words, gestures, and tone of voice in a multitude of situation. Would you talk to a small child with the same words you would in a business meeting. Being able to communicate...

...The Language Used to Connect With Nature
Willa Cather, Emily Dickinson, and Walt Whitman all utilize different forms of language to make themes in their writings. Through personification, symbolism, and various rhetorical devices, we can connect to nature through O Pioneers!, “There’s a Certain Slant of Light,” and “Song of Myself.” These languages are used in these pieces to connect us with nature.
Cather uses personification to connect us to...