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DFA & RE from descriptive definition of given regular language

I am trying to make the DFA and RE of a regular language which is define on the alphabet = {1,0} and all the strings present in these languages have exactly one 010 substring in them.

Some strings which are accepted by the above regular language are;

{010, 0100, 0101, 1010, 0010 …….0101110…..}

In the above strings there is only one 010 substring. If there is more than one 010 substring in a string such as.

{01010, 01011010… }

then the DFA of the above language should not accept that string.

If someone provide me ony DFA of the above lang. then i would be able to make the RE by state elimination. Or if someone provide me the RE of the above lang. then i could make the DFA by other kleene theorem.

Note: I go through the question which is already on the CS stackexchange as previously my question was marked duplicate. This question is about “How we can prove that a given language is regular or not”. But in my question i have provided the descriptive definition of a regular language. And i am trying to get its RE or DFA.

DFA & RE from descriptive definition of given regular language [duplicate]

• How to prove a language is regular? 8 answers

I am trying to make the DFA and RE of a regular language which is define on the alphabet = {1,0} and all the strings present in these languages have exactly one 010 substring in them.

Some strings which are accepted by the above regular language are;

{010, 0100, 0101, 1010, 0010 …….0101110…..}

In the above strings there is only one 010 substring. If there is more than one 010 substring in a string such as.

{01010, 01011010… }

then the DFA of the above language should not accept that string.

If someone provide me ony DFA of the above lang. then i would be able to make the RE by state elimination. Or if someone provide me the RE of the above lang. then i could make the DFA by other kleene theorem.

What is the motivation behind ” Descriptive Complexity “?

Time and Space are two commons parameters (and also natural parameters) to measure the complexity of the problem. I am not able to understand the motivation behind defining ” Descriptive Complexity”. I search on the internet and find out that it is the complexity of expressing some property of the input. Take the example of the sorting problem. Time and Space seems to be a natural choice. I am unable to come up with an example or a problem which immediately implies the importance of defining the ” Descriptive Complexity “.

Question : What is the motivation behind ” Descriptive Complexity “?

Structure of numbers in descriptive complexity

Descriptive complexity is a useful way to free yourself from computational considerations when studying complexity. One of those considerations is the encoding of the structures you are working on.

However, the way we usually see integers in descriptive complexity is exactly the same way we’re used to with Turing machines : $$n$$ is an ordered set of $$\log_2 n$$ elements, together with a unary relation that is true on the $$i$$-th element iff the $$i$$-th bit is 1 in the binary representation of $$n$$. This means we see integers exactly as their encodings.

Moreover, one of the main questions in descriptive complexity is Chandra-Harel conjecture, i.e. is there a logic for P on unordered structures. As such, is there a way to see integers as unordered structure ? Such a way should still ensure that the encoding of an integer is (at least poly-)logarithmic in $$n$$.

When do we use prescriptive vs descriptive models?

In design methodology we can use descriptive models such as hierarchical task analysis and we use prescriptive models such as user stories to capture and understand the context of use as well as the user mental model.

The question is, how do we use them appropriately? meaning when and why do we use either descriptive/prescriptive models?