Example: Examples of NFA

(related to Chapter: Finite Automata (Finite Sequential Machines))

Non-deterministic finite automata can be illustrated using diagrams like it was the case for the DFA.

Example 1 - Every DFA is an example of an NFA

Please note that the NFA definition is more general than the DFA definition since it replaces a function $\delta$ by a relation $\Delta$ (every function is a relation but not every relation is a function).

Example 2

The following example of an NFA accepts all strings over the alphabet $\{0,1\}$ whose second to the last symbol is $1.$

nfa1

Note that the same strings can be accepted by this, more complex, DFA:

dfa5

Example 3

The following example of an NFA accepts all strings over the alphabet $\{0,1\}$ that are concatenations of $10$ and $101$. In other words, the language accepted by the NFA is $\{10,101\}^*$:

nfa2

As in example 2, the same strings can be accepted by another, much more complex, DFA:

dfa6

Applications: 1
Theorems: 2


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References

Bibliography

  1. Erk, Katrin; Priese, Lutz: "Theoretische Informatik", Springer Verlag, 2000, 2nd Edition
  2. Hoffmann, Dirk: "Theoretische Informatik, 3. Auflage", Hanser, 2015