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Unformatted text preview: cs3102: Theory of Computation Class 4: Nondeterminism Spring 2010 University of Virginia David Evans PS1 is due now! Adding Nondeterminism 1 2 Deterministic machine: at every step, there is only one choice Nondeterministic machine: at some steps, there may be more than one choice. a a, b b b Nondeterminism in Practice Nondeterminism in Theory Omnipotent: Machine splits into a new machine for each choice; if any machine accepts, accept. Omniscient: Whenever it has to make a choice, machine always guesses right. Example NFA 1 2 3 a b a, b Defining DFAs A deterministic finite automaton is a 5-tuple: Q finite set (“states”) Σ finite set (“alphabet”) δ : Q × Σ → Q transition function q ∈ Q start state F ⊆ Q set of accepting states How do we need to change this to support nondeterminism ? Defining N FAs A non deterministic finite automaton is a 5-tuple: Q finite set (“states”) Σ finite set (“alphabet”) transition function q ∈ Q start state F ⊆ Q set of accepting states Output of transition function is a set of states, not just one state....
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- Spring '08
- Regular expression, Regular language, Nondeterministic finite state machine, Automata theory