Deterministic Finite State Automaton Construction

In summary, a Deterministic Finite State Automaton (DFA) is a mathematical model used to recognize patterns within input strings. It consists of a finite set of states, a set of input symbols, a transition function, a start state, and a set of accept states. To construct a DFA, you must define these components and map out the transitions between states for each input symbol. The main difference between a DFA and a Non-Deterministic Finite State Automaton (NFA) is that an NFA can have multiple possible next states for a given input symbol, while a DFA can only have one. DFAs have various applications in computer science, including lexical analysis, pattern recognition, and natural language processing. However, they have limitations
  • #1
francis21
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Homework Statement


Find a simple DFA (i.e. deterministic finite automaton) that accepts all natural numbers n for which n mod 3 = 0.

Hint: A natural number is divisible by 3 if its checksum (or sum of digits) is divisible by 3.


Homework Equations





The Attempt at a Solution



I'm not sure how the hint can help for this question, even though I know what it means. For instance, 137 = 1+3+7 = 11 mod 3 ≠ 0 etc.

Any other useful hints or suggestions would be great. Thanks. :)
 
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  • #2
I have finally solved the problem, so its all good now.

Can the admin close this thread down. Thanks.
 

FAQ: Deterministic Finite State Automaton Construction

What is a Deterministic Finite State Automaton (DFA)?

A Deterministic Finite State Automaton, also known as a Deterministic Finite Automaton (DFA), is a mathematical model used to recognize patterns within input strings. It consists of a finite set of states, a set of input symbols, a transition function, a start state, and a set of accept states. The DFA reads input symbols and transitions between states based on the transition function until it reaches an accept state, indicating that the input string is accepted.

How is a DFA constructed?

To construct a DFA, you must first define the set of states, the input alphabet, the transition function, the start state, and the set of accept states. Then, using a transition table or diagram, you can map out the transitions between states for each input symbol. The DFA must be deterministic, meaning that for each state and input symbol, there can only be one possible next state.

What is the difference between a DFA and a Non-Deterministic Finite State Automaton (NFA)?

The main difference between a DFA and an NFA is that an NFA can have multiple possible next states for a given input symbol, while a DFA can only have one. This means that an NFA is non-deterministic, and can potentially have more than one path to reach an accept state for a given input string. Additionally, an NFA can have empty transitions, where no input symbol is read to transition between states.

What are some real-world applications of DFAs?

DFAs have a wide range of applications in computer science, including lexical analysis in compilers, pattern recognition, and natural language processing. They are also used in circuit design, software verification, and network security. In addition, DFAs can be used to model and analyze the behavior of complex systems, such as biological systems and social networks.

What are some limitations of DFAs?

One limitation of DFAs is that they can only recognize regular languages, which are a subset of all possible languages. This means that they cannot handle more complex languages, such as context-free or context-sensitive languages. Additionally, DFAs can become large and complicated when trying to recognize certain patterns, making them impractical for some applications. Finally, constructing a DFA for a given language can be a challenging and time-consuming task, especially for more complex languages.

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