Theory of Computation Question

In summary, the conversation discusses the creation of state diagrams for DFAs recognizing a language where the alphabet is {0,1}. The language requires that the input has a length of at least 3 and its third symbol is a 0. The conversation also discusses the efficiency of the solution and the possibility of needing a fourth state.
  • #1
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Homework Statement



Give state diagrams of DFAs recognizing the following languages. In all parts the alphabet is {0,1}.

{w | w has length at least 3 and its third symbol is a 0}

Homework Equations



If the final state only has one circle it is rejected, if two, accepted.

The Attempt at a Solution



aqr05.jpg


I am just wondering if this is the most efficient way of doing this problem, or do I have too many states?

Oh also, I forgot to add an arrow pointing to qs indicating the start.
 
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  • #2
I think you'll agree that there may not be less than three states because one needs to track how much of the input has been seen. The only way to do this is to have independent states for the first three characters. Only on the third character may we check for the final 0.

Is another state required? See if you can you argue that because an accepting state is required, and because none of the first three states may be accepting states, a fourth state is necessary.
 

1. What is the Theory of Computation?

The Theory of Computation is a branch of computer science that deals with the study of algorithms, mathematical models, and computational systems. It seeks to understand the capabilities and limitations of different computation models and how to efficiently solve problems using these models.

2. What are the main components of the Theory of Computation?

The main components of the Theory of Computation include automata theory, computability theory, and complexity theory. Automata theory studies abstract computing devices and their capabilities, while computability theory focuses on what problems can be solved by these devices. Complexity theory deals with the resources required to solve a problem, such as time and space.

3. How is the Theory of Computation relevant to computer science?

The Theory of Computation is essential to computer science as it provides a theoretical foundation for understanding and analyzing algorithms and their efficiency. It also helps in developing new computational models and solving complex problems in different areas of computer science, such as artificial intelligence, cryptography, and database systems.

4. What are some real-world applications of the Theory of Computation?

The Theory of Computation has numerous real-world applications, such as in designing efficient algorithms for search engines, data compression, and encryption. It is also used in the development of programming languages and in the study of artificial intelligence and machine learning.

5. What are some challenges in the Theory of Computation?

Some of the challenges in the Theory of Computation include solving complex problems efficiently, determining the limits of computation, and understanding the relationship between different computational models. There are also ongoing efforts to develop new computational models that can solve problems more efficiently than existing ones.

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