Venn Diagram Examples for Problem Solving.
Computer Science. Chomsky Hierarchy

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A Venn diagram, sometimes referred to as a set diagram, is a diagramming style used to show all the possible logical relations between a finite amount of sets. In mathematical terms, a set is a collection of distinct objects gathered together into a group, which can then itself be termed as a single object. Venn diagrams represent these objects on a page as circles or ellipses, and their placement in relation to each other describes the relationships between them.

Draw the Venn diagrams for problem solving in computer science using the ConceptDraw PRO diagramming and vector drawing software extended with the Venn Diagrams solution from the area "What is a Diagram" of ConceptDraw Solution Park.

Venn Diagram Solution

Example 1. Venn Diagrams Solution

The Venn diagram example below visualizes the the class of language inclusions described by the Chomsky hierarchy.

"Within the field of computer science, specifically in the area of formal languages, the Chomsky hierarchy (occasionally referred to as Chomsky-Schützenberger hierarchy) is a containment hierarchy of classes of formal grammars. This hierarchy of grammars was described by Noam Chomsky in 1956. It is also named after Marcel-Paul Schützenberger, who played a crucial role in the development of the theory of formal languages. The Chomsky Hierarchy, in essence, allows the possibility for the understanding and use of a computer science model which enables a programmer to accomplish meaningful linguistic goals systematically." [Chomsky hierarchy. Wikipedia]

Example 2. Venn Diagram Problem Solving - Chomsky Hierarchy

A graphical representation of the sets of languages included in the Chomsky hierarchy.

"The Chomsky hierarchy consists of the following levels:

  • Type-0 grammars (unrestricted grammars) include all formal grammars. They generate exactly all languages that can be recognized by a Turing machine. These languages are also known as the recursively enumerable languages.
  • Type-1 grammars (context-sensitive grammars) generate the context-sensitive languages. ... The languages described by these grammars are exactly all languages that can be recognized by a linear bounded automaton (a nondeterministic Turing machine whose tape is bounded by a constant times the length of the input.)
  • Type-2 grammars (context-free grammars) generate the context-free languages. ... These languages are exactly all languages that can be recognized by a non-deterministic pushdown automaton. Context-free languages – or rather the subset of deterministic context-free language – are the theoretical basis for the phrase structure of most programming languages, though their syntax also includes context-sensitive name resolution due to declarations and scope. Often a subset of grammars are used to make parsing easier, such as by an LL parser.
  • Type-3 grammars (regular grammars) generate the regular languages."
    [Chomsky hierarchy. Wikipedia]

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Use Solution:

  • Design Venn Diagrams
  • Intuitive way to work with sets
  • Shows all possible logical relations
  • To teach elementary set theory
  • Illustrate set relationships in probability
  • Illustrate logic
  • Illustrate statistics
  • Illustrate linguistics
  • Illustrate computer science
  • Design elements for Venn Diagrams
  • Venn Diagram template and examples
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  • Export to vector graphics files
  • Export to Adobe Acrobat® PDF
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  • Cross Platform Compatibility
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