# l2 - Lecture 2 Finite Automata David L Dill Department of...

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Lecture 2: Finite Automata David L. Dill Department of Computer Science 1

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Outline Introduction to regular languages. Deterministic finite automata (DFA) Nondeterministic finite automata (NFA) Proof that NFA and DFA languages are the same (subset construction). 2
Motivation The next few lectures will be about Regular languages . Regular languages can be infinite, and can be described in several ways: by deterministic or non-deterministic finite automata, or by regular expressions. Regular languages are of great practical as well theoretical importance. Widely used in applications (compilers, pattern matching, specification and formal verification of systems). Constructions from automata theory are used in these applications. Basis for more sophisticated representations (automata on infinite strings, tree automata, timed automata). Decidable – Many problems on finite automata are solvable. (membership, emptiness, universality, subset, etc.) We’ll have lots of positive results with regular languages. Later, the most important results will be negative. “More expressiveness” leads to “harder problems.” 3

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Deterministic Finite Automata A finite automaton is a mathematical model of a machine that reads strings and says “yes” or “no” for each string. A DFA defines an infinite language: the set of strings for which it says “yes.” q2 0 q0 1 1 q1 0 0 1 4
Deterministic Finite Automata A DFA is a quintuple: ( Q, Σ ,q 0 ,δ,F ) where Q is a finite set of states. Σ is an alphabet. q 0 Q is a start state. δ : Q × Σ Q a next-state function. A set of final states F Q . ( Students: make sure you know what all these are in the diagram on the previous slide. ) 5

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Language of a DFA We extend the next state function δ to work on whole strings. For our example DFA in slide 4, ˆ δ ( q 1 ) = q 1 ˆ δ ( q 0 , 010101000)
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l2 - Lecture 2 Finite Automata David L Dill Department of...

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