Thompson's construction algorithm
So imagine you are playing with blocks (like Legos) and you want to build a castle. But instead of having a blueprint to follow, you only have some rules on how the blocks can be put together. For example, some blocks can only be placed on top of others, and some can be beside each other.
The Thompson's construction algorithm is like creating a blueprint for this castle using these rules. But instead of blocks, we are dealing with something called regular expressions, which are a way of describing patterns in text.
So let's say we have a regular expression that says we want to match the word "cat". The blueprint for this would be a machine that has three states:
1. Start state: this is the beginning state where we haven't matched anything yet.
2. State for 'c': if we see the letter 'c' in the text, we move to this state.
3. State for 'a' and 't': if we see the letters 'a' and 't' in sequence, we move to this state.
So now we have a machine that matches the word "cat" in any text. But what if we have a more complex regular expression like "foo|bar"? This means we want to match either "foo" or "bar".
The blueprint for this would be a machine with three states again:
1. Start state
2. State for 'f' and 'b': if we see the letters 'f' or 'b', we move to this state.
3. State for 'o' or 'a' and 'r': if we see the letters 'o' after 'f' or 'a' and 'r' after 'b', we move to this state.
So now we have a machine that can match either "foo" or "bar" in any text. This is basically what the Thompson's construction algorithm does: it converts a regular expression into a state machine that can match that pattern in any text.
The Thompson's construction algorithm is like creating a blueprint for this castle using these rules. But instead of blocks, we are dealing with something called regular expressions, which are a way of describing patterns in text.
So let's say we have a regular expression that says we want to match the word "cat". The blueprint for this would be a machine that has three states:
1. Start state: this is the beginning state where we haven't matched anything yet.
2. State for 'c': if we see the letter 'c' in the text, we move to this state.
3. State for 'a' and 't': if we see the letters 'a' and 't' in sequence, we move to this state.
So now we have a machine that matches the word "cat" in any text. But what if we have a more complex regular expression like "foo|bar"? This means we want to match either "foo" or "bar".
The blueprint for this would be a machine with three states again:
1. Start state
2. State for 'f' and 'b': if we see the letters 'f' or 'b', we move to this state.
3. State for 'o' or 'a' and 'r': if we see the letters 'o' after 'f' or 'a' and 'r' after 'b', we move to this state.
So now we have a machine that can match either "foo" or "bar" in any text. This is basically what the Thompson's construction algorithm does: it converts a regular expression into a state machine that can match that pattern in any text.