CSC 360 Finite Automata Deterministic, Nondeterministic

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CSC 360 Finite AutomataDeterministic,
Non-deterministic

• Dr. Curry Guinn

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Todays Class

• Finite Automata
• Examples
• Complementary languages
• Non-determinism

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Examples

• (ab)
• (a)b
• (a)b(a)
• (ab)b(ab)
• (ab)bb(ab)
• (ab)((aa)(bb))(ab)
• Two as, odd number of bs
• Even as, odd number of bs

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Incompletely specified DFA

• Example 5.3.9
• Equivalent machines

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Deterministic Finite Automaton (DFA)

• A deterministic finite automaton is a quintuple M
  (Q, S, ?, q0, F) where
• Q is a finite set of states,
• S a finite set called the alphabet,
• q0 ? Q a distinguished state known as the start
  state,
• F a subset of Q called the final or accepting
  states, and
• ? a total function from Q X S to Q known as the
  transition function.

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Non-deterministic Finite Automaton (NFA or
sometime nDFA)

• A nondeterministic finite automaton is a
  quintuple M (Q, S, ?, q0, F) where
• Q is a finite set of states,
• S a finite set called the alphabet,
• q0 ? Q a distinguished state known as the start
  state,
• F a subset of Q called the final or accepting
  states, and
• ? a total function from Q X S to P(Q) known as
  the transition function.

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Non-deterministic examples

• (a ? b)bb
• (a ? b)(aa ? bb) (a ? b)

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?-Transitions

• ?(q1, ?) q2 may be defined.
• L1 (ab)bb(ab)
• L2 (ab)aa(ab)
• What is the machine for L1 ? L2?
• How about L1 concatenated to L2?

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Using ?-transitions

• All strings of even length over a,b

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A Koan

• If a tree falls in a forest, does it make a
  sound?
• Definition 1 Sound is vibration, as perceived by
  the sense of hearing
• Definition 2 Mechanical energy vibrations
  transmitted as waves through a solid, liquid, or
  a gas that can be detected by the human ear

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Another koan

• Does the written sentence Computer Science is a
  challenging major mean anything if no one reads
  it?
• Does a sentence have intrinsic meaning?
• Where does the meaning of the sentence reside?

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Koan 3

• On torvalds, I have a copy of your 16.pl file.
• Does that 16.pl file have any meaning?
• Does it have any meaning if it is never run?
• Does it have any meaning if no human ever reads
  it?
• Does it have any meaning if no machine ever reads
  it?

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GEB, Chapter 6

• Does a record album (how quaint) with a recording
  of Bach have meaning intrinsically?
• Is the jukebox necessary for the album to have
  meaning?

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Voyagers Golden Record

• http//voyager.jpl.nasa.gov/spacecraft/goldenrec.h
  tml
• http//voyager.jpl.nasa.gov/

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DNA

• Is there meaning in DNA molecules?
• What is genotype? Phenotype?
• What does epigenesis mean?
• Cell differentiation
• The Epigenesis of Meaning in Human Beings, and
  Possibly in Robots

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For Next Class, Thursday

• Homework 6 due at the beginning of class,
  Tuesday, March 11
• Thursday, Sudkamp, Chapter 5.6
• Removing Nondetermism
• GEB
• Chapter 7, The Propositional Calculus (also
  called first-order predicate logic)