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Phase 4 task 2 - schwappach

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Phase 4 task 2 - schwappach

Phase 4 task 2 - schwappach

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  • 1. Colorado Technical University MAT200, OLA: Discrete Mathematics Professor: Ricky Streight Created: 20 June 2008 Presented by: TSgt Loren K. R. Schwappach Major: Electrical EngineeringNOTE: Please Use MS Power Point version 2007 for full compatibility with slides.
  • 2. Topic #1: Languages What are † Languages?:  Formal Language: Wikipedia defines a formal language as an organized set of symbols that can be precisely defined in terms of the shapes and locations of the symbols. Colorado Technical University explains a formal language is like a set of strings produced from a finite alphabet, and uses the English language as an example. The set of stings would include all of the words making up the language.  For example the string l-i-f-e is the word life and is a part of the English language while the string r-x-x-r-q-q-z has no meaning in the English language.  Language set notation: Formal languages are defined by rules the language must obey. Thus set notation provides a powerful method for logically approaching formal languages.
  • 3. Topic #1: Languages: Examples
  • 4. Topic #2: GrammarWhat are † Formal Grammars?:  Defined: Wikipedia says a formal grammar is a precise description of a formal language. Grammar describes which of the possible sequences of symbols (strings) in a language constitute valid words or statements in a language, but does not describe their semantics. Wikipedia, 2008)  In other words grammar is the glue that makes the strings (words) in a formal language work together.  Backus-Naur form (BNF): One of the most common methods used to describe a formal language. Wikipedia classifies BNF as a meta- syntax used to express context-free grammars.  BNF describes how a sentence is produced using a form known as productions. Using BNF language strings can be made into sentences  The best way to understand BNF is with a quick example.
  • 5. Topic #2: Grammar: Examples
  • 6. Topic #3: Automata What is † Automata Theory?:  Defined: The study of abstract machines and the problems they are able to solve. (Wikipedia, 2008)  Deterministic finite automata: An automata that has a transition for every letter of the alphabet and where a state cannot have multiple outgoing edges with the same label.  Nondeterministic finite automata: An automata that may or may not have a transition for every letter in the alphabet, or multiple transitions and where a state can have multiple outgoing edges all with the same label.  Automaton: A mathematical model of a finite-state machine † in which the set of output symbols is {0,1} and where the current state determines the last output. (Johnsonbaugh, 2009)  A finite-state machine (FSM) is a machine that, given an input of symbols “jumps” through a series of states according to a transition function (which can be expressed as a table). (Wikipedia, 2008)
  • 7. Topic #3: Automata: Examples S0 S1 S2 S3
  • 8. Topic #3: Automata: Examples S0 S1 S2
  • 9. CTU Online, (2008). Multimedia Material, Retrieved Jun, 19, 2008, from Colorado Technical University Web site: https://campus.ctuonline.eduJohnsonbaugh, R. (2009). Discrete Mathematics (7th ed.). Upper Saddle River, New Jersey: Pearson Prentice Hall.Rizzi, R. (2002). Complexity of Context-free Grammars with Exceptions and the inadequacy of grammars as models for XML and SGML. Massachusetts Institute of Technology.Wikipedia. (2008). Automata theory. Retrieved Jun, 9, 2008, from Wikipedia the free encyclopedia Web site: http://en.wikipedia.org/wiki/Automata_theoryWikipedia. (2008). Automaton. Retrieved Jun, 9, 2008, from Wikipedia the free encyclopedia Web site:http://en.wikipedia.org/wiki/AutomatonWikipedia. (2008). Backus-Naur Form. Retrieved Jun, 9, 2008, from Wikipedia the free encyclopediaWeb site: http://en.wikipedia.org/wiki/Backus-Naur_formWikipedia. (2008). Formal_grammar. Retrieved Jun, 9, 2008, from Wikipedia the free encyclopediaWeb site: http://en.wikipedia.org/wiki/Formal_grammar
  • 10. If you have any questions or suggestions Please email me at: Loren.Schwappach@peterson.af.mil or Lschwappach@yahoo.com