Lecture 2 (Kani) - Deterministic finite automata (DFAs)

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September 03 2024 Lecture 2 (Kani) - Deterministic finite automata (DFAs) Lecture 2 (Kani) - Deterministic finite automata (DFAs) Lecture 2 (Kani) - Deterministic finite automata (DFAs) Lecture 2 (Kani) - Deterministic finite automata (DFAs)
 

Notes

Deterministic Finite Automata

Graphical Representation:

Example2

Definitions:

Formal Definitions:

Theorems

Languages accepted by DFAs are closed under compliment

If $L$ is accepted by $M_1 = (Q, \Sigma, s, A, \delta)$, then $\bar{L}$ is accepted by $M_2 = (Q, \Sigma, s, \bar{A}, \delta)$ where

Example:

Example2

Languages accepted by DFAs are closed under intersection

If $L_1$ is accepted by $M_1 = (Q_1, \Sigma, s_1, A_1, \delta_1)$ and $L_2$ is accepted by $M_1 = (Q_1, \Sigma, s_2, A_2, \delta_2)$ then $L_1 \cap L_2$ is accepted by $M = (Q, \Sigma, s, A, \delta)$ where

Example:

Example3

Languages accepted by DFAs are closed under union

If $L_1$ is accepted by $M_1 = (Q_1, \Sigma, s_1, A_1, \delta_1)$ and $L_2$ is accepted by $M_1 = (Q_1, \Sigma, s_2, A_2, \delta_2)$ then $L_1 \cap L_2$ is accepted by $M = (Q, \Sigma, s, A, \delta)$ where

Example:

Example4

Constructing Regular Expressions from DFAs

In depth in Lecture 5

State Elimination: Slides 28-31 (55-60)

Algebraic Method: Slides 34-37 (64-68)

 

Additional Resources

Contributors

Nicholas Bampton