Nondeterministic Finite Automata (Firday October 6 2006)

Class was cancelled on August 1, Monday. Wednesday's class was a problem-solving session

Nondeterministic Finite Automata.

Formal definition. (Important Understand the formalism of the transistion function. It eventually maps sets of states and a symbol into a set of states.)

The main theorem: nondeterministic automata accept only regular languages.
Proof idea: the collection of subsets of a finite set is finite. See the definition of the transition function of a nondeterministic automaton: it is a deterministic automaton if subsets of states are viewed as a "STATE".

Epsilon-transitions.
Theorem: still accepts only regular languages.
BUT much easier to prove some theorems, like the closure properties below.

Closure properties of regular languages

• union
• intersection
• complement
• concatenation
• star (asterate)

Proofs by pictures of nfa with epsilon-transitions.