Terminal Symbol Set

A Terminal Symbol Set is a Formal Alphabet (composed of Terminal Symbol) that is associated to a Formal Grammar.

• AKA: Formal Grammar Terminal Symbol Set, Σ, T.
• Context:
  • It can be Disjoint from a Non-Terminal Symbol Set.
  • It can be a Member of:
    • a Context-Free Grammar.
• Example(s):
  • a Natural Language Word Form Set.
• See: Non-Terminal Symbol Set.

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References

• http://www.csee.umbc.edu/help/theory/lang_def.shtml
  • Alphabet
    • A finite set of symbols.
    • An alphabet is often denoted by sigma, yet can be given any name.
    • B = {0, 1} Says B is an alphabet of two symbols, 0 and 1.
    • C = {a, b, c} Says C is an alphabet of three symbols, a, b and c.
    • Sometimes space and comma are in an alphabet while other times they are meta symbols used for descriptions.

2007

• (Kakkonen, 2007) ⇒ Tuomo Kakkonen. (2007). “Framework and Resources for Natural Language Evaluation." Academic Dissertation. University of Joensuu.
  • Definition 3-1. Symbol, terminal and alphabet.
    • A symbol is a distinguishable character, such as “a”, “b” or “c”.
    • Any permissible sequence of symbols is called a terminal (also referred to as a word).
    • A finite, nonempty set ∑ of terminals is called an alphabet.
  • Definition 3-2. String and sets of strings.
    • Let Σ be an alphabet.
    • A finite sequence of symbols S=(x1 x2… xn), n≥0, x∈Σ is called a string in alphabet Σ.
    • The length |S| of string S is n.
    • The empty string is the sequence of length 0; written ε.
    • Σ* is the set of all strings in Σ.
    • In addition, Σ+ = Σ*- {ε}.
  • Definition 3-3. Language and sentence.
    • Let Σ be an alphabet.
    • Any subset [math]\displaystyle{ L }[/math] of Σ* is called a language over alphabet Σ.
    • Sequence δ = (α1 α2 … αn), where αi ∈ L∀i, 1≤i≤n, n' ∈ natural numbers, is called a sentence in language L.

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