Optimizing and minimization of a Deterministic Finite Automata

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  • #1
gratusri
1
0
Thread moved from the technical math forums to the schoolwork forums
so this is the question , I have to minimize this DFA

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this is How I did it

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but when I checked for answers , this is what it was,
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can someone please explain to me what mistake I made? I have been wondering about this for past 2 days
 
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  • #2
gratusri said:
can someone please explain to me what mistake I made?
No idea but your answer is not even a single DFA. The book answer is clearly correct and can be determined quickly by inspection*: are you sure you are expected to use an eigenvalue method to get to the answer?

*Note that there are no paths to q2 and q4 and q3 accepts so the path to q5 is irrelevant
 

FAQ: Optimizing and minimization of a Deterministic Finite Automata

What is the purpose of optimizing a Deterministic Finite Automaton (DFA)?

The purpose of optimizing a DFA is to reduce the number of states and transitions, making the automaton more efficient in terms of memory usage and computational performance. This can be crucial in applications where resources are limited or where the DFA is part of a larger system that requires high efficiency.

What are the common methods used for minimizing a DFA?

Common methods for minimizing a DFA include the Myhill-Nerode Theorem, which partitions the states into equivalence classes, and Hopcroft's algorithm, which is an efficient algorithm for finding the minimal DFA. Other methods include Brzozowski's algorithm and Moore's algorithm.

How do you determine if two states in a DFA are equivalent?

Two states in a DFA are considered equivalent if, for every input string, they transition to the same state or an equivalent state. This means that the DFA behaves identically starting from either state for any input sequence. Equivalence can be determined using methods like the Myhill-Nerode Theorem or partition refinement techniques.

Can minimizing a DFA change the language it recognizes?

No, minimizing a DFA does not change the language it recognizes. The minimized DFA is equivalent to the original DFA in terms of language recognition; it simply has fewer states and transitions. The optimization process ensures that the minimized DFA accepts the same set of strings as the original DFA.

What are the practical applications of DFA minimization?

Practical applications of DFA minimization include compiler design, where minimized DFAs are used for lexical analysis to recognize tokens efficiently. It is also used in network security for pattern matching in intrusion detection systems, text processing, and various fields of computational linguistics and artificial intelligence where efficient pattern recognition is required.

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