HyClt310s2008: Exercises

Task 1

Describe the following properties using Monandic Second Order Logic that is interpreted over finite strings:
  • Even-Parity
  • Length-Is-Multiple-Of-Three
  • "invent" new examples of interest to your domain
    • Lexc-String:
      • Informally: A string starting from @Root@ ending in @#@, internally made of series of alphabets A or exact pairs of joiners J; e.g. @Root@kissa@case@@case@lla@#@ is a valid Lexc-String.
      • Broken solution(?): Lexc-String(L) ≝ string(L) ∧ ∀ x ∈ L ∃ y ∈ L, z ∈ Σ | alphabet(x) ∨ (symbol(x, z) ∧ symbol(y, z) ∧ (xor(succ(x, y), succ(y, x))) ∨ (first(x, L) ∧ starter(x)) ∨ (last(x, L) ∧ ender(x)))
      • xor(E, F) ≝ (E ∧ F) ∨ (E ∧ F)
      • alphabet(x) ≝ symbol(x, a) ∨ symbol(x, b) ∨ …, for finite set of alphabet?
      • joiner(x), ender(x), and starter(x) similarly
      • Notation is surely flawed as I haven’t dealt with mathematics or logic in ages. For that and other problems e.g. ones mentioned in lectures, do suggest improvements – TommiPirinen
      • (The windows systems at department seem to have broken math fonts; assume ∧ = and, ∨ = or)


-- AnssiYliJyra - 2008-10-31
Topic revision: r4 - 2008-11-25 - TommiPirinen
 
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