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...

...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...

...Prepositions – Time
|English |Usage |Example |
|on |days of the week |on Monday |
|in |months / seasons |in August / in winter |
| |time of day |in the morning...

...Running head: LANGUAGE ACQUISITION THEORIESLanguage Acquisition Theories
Donelle Brown
Grand Canyon University
ESL 533N
March 23, 2009
Language Acquisition Theories
Acquiring the necessary English vocabulary to succeed in the United States is very difficult for the ELL or ESL student. It takes time and patience on their and the part of their families. Of course, with most of these...

...LANGUAGE ACQUISITION THEORIESLANGUAGE ACQUISITION
Language acquisition is the process by which humans acquire the capacity to perceive, produce and use words to understand and communicate.
The acquisition of language is doubtless the greatest intellectual feat any one of us is ever required to perform. (Leonard Bloomfield, Language1993)
THEORIES OF LANGUAGE ACQUISITION
Theory...

...THEORIES OF LANGUAGE ACQUISITION.
Over the last fifty years, several theories have been put forward to explain the process by which children learn to understand and speak a language. They can be summarized as follows:
Theory
Central Idea
Individual most often
associated with theory
Behaviourist
Children imitate adults. Their correct utterances are reinforced when they get what they want or are praised....

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