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 language as opposed to natural language must be used with computer applications because natural language is too vague for computer applications. Automata is a way to test an expression to determine if it is part of the language (Pfeifer, 2005). A deterministic finite automata (DFA) is a machine that is the most simple to understand which will help with the more complicated machines because many important properties of the DFA are found in the more complicated machines. DFA’s are found in many things like vending machines and elevators. The DFA works starting in a ‘start state’ then by reading a string, then producing an output of true or false according to how the machine is setup. As long as there is data entering the machine the output will change according to what was read in and how the configuration of the machine states what the output reports. A deterministic algorithm will always run the same way each time with the input of identical information (Sedgewick, n.d.). The difference between deterministic finite state automata and nondeterministic finite state automata is a DFA can only be in one state at a time when the nondeterminism happens when there is more than one choice of state (LaValle, 2006). A formal language is defined by alphabet and formation rules. The alphabet is built on a set of symbols that can have special meaning. The formation of the symbols will define well-formed strings which are called words, expressions, formulas or terms (Sakharov, n.d.). Examples of language formation rules are the proposition, p^q, and negation, ~p V ~q. The...

...Finite Automata
Finite Automata
• Two types – both describe what are called regular languages
– Deterministic (DFA) – There is a fixed number of states and we can only be in one state at a time – Nondeterministic (NFA) –There is a fixed number of states but we can be in multiple states at one time
• While NFA’s are more expressive than DFA’s, we will see that adding nondeterminism does not let us define any language that cannot...

...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...

...INTERNATIONAL J OURNAL OF M ULTIDISCIPLINARY S CIENCES AND ENGINEERING, VOL . 3, NO. 5, M AY 2012
Computing Game Design with AutomataTheory
Noman Sohaib Qureshi1, Hassan Mushtaq2, Muhammad Shehzad Aslam2, Muhammad Ahsan2, Mohsin Ali2 and Muhammad Aqib Atta2 the designed automata is divided into weapon, select, move, action and game sets. States are assigned labels or tags and are explained. The state routing in game is smooth at from level one to...

...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...

...1. THEORY OF LANGUAGE
The theory of language underlying Duysel Learning was derived from a view of proposed by Turkish Linguistics in the 2000s. Duysel Learning Method involves both the learning of language knowledge and the cultivation of language skills, with the emphasis on both the form and the content of a language. In teaching practice, its all-inclusive nature requires English teachers...

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Finite-State Machines and Pushdown Automata
The ﬁnite-state machine (FSM) and the pushdown automaton (PDA) enjoy a special place in computer science. The FSM has proven to be a very useful model for many practical tasks and deserves to be among the tools of every practicing computer scientist. Many simple tasks, such as interpreting the commands typed into a keyboard or running a calculator, can be modeled by ﬁnite-state machines. The PDA is a model to...

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Deque Automata for all classes of Formal languages
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...

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