If you want to try your hand at AI, this is a good case to work on it with. One application (of many) is control-flow-structure synthesis, because that’s what this really is, in disguise. The states are goto-labels, the embedded state-labels are “goto’s”, the stars are loops, the “+”‘s are branches, either deterministic, if “guarded” or non-deterministic. Here is the first step (note that a self loop with a label $a$ would have transformed the first $ε$ into $(ε+a)$.
One way to implement regular expressions is to convert them into a finite automaton, known as an ∈-NFA (epsilon-NFA). An ∈-NFA is a type of automaton that allows for the use of “epsilon” transitions, which do not consume any input. This means that the automaton can move from one state to another without consuming any characters from the input string.
Transitive closure method
Here I will describe the one usually taught in school which is very visual. However, writing the algorithm is not such a good idea. The solution is a set of regular expressions $Q_i$, one for every state $q_i$. $Q_i$ describes exactly those words that can be accepted by $A$ when started in $q_i$; therefore $Q_0$ (if $q_0$ is the initial state) is the desired expression. The main pattern can be seen in the following to figures. The first has labels between $p,q,r$ that are regular expressions $e,f,g,h,i$ and we want to remove $q$.
The algorithm
Check out this repo, it translates your regular expression to an NFA and visually shows you the state transitions of an NFA. Given the complexity of the file – even with the expression sharing – you can begin to see why I never (yet) got around to writing a reverse convertor. You need heuristics to optimize the algebraic systems and expressions … So, I’ve been sorta sitting on this (RegEx is from the mid 1990’s, originally posted in the comp.compilers archives), waiting for AI to come around.
- All the images above were generated using an online tool for automatically converting regular expressions to non-deterministic finite automata.
- The idea is to consider regular expressions on edges and then removing intermediate states while keeping the edges labels consistent.
- I will describe it using higher-level primitives.
- Step 2 Remove Null transition from the NFA and convert it into its equivalent DFA.
How to convert finite automata to regular expressions?
Converting regular expressions into (minimal) NFA that accept the same language is easy with standard algorithms, e.g. The other direction seems to be more tedious, though, and sometimes the resulting expressions are messy. Even if it may seems a system of equations that seems too symbolic for an algorithm, this one is well-suited for an implementation.
Construction of an FA from an RE
You buy sell and trade cryptocurrency instantly should not remove final or initial states lightly, otherwise you will miss parts of the language. This algorithm is about handling the graph of the automaton and is thus not very suitable for algorithms since it needs graph primitives such as … I will describe it using higher-level primitives. Step 2 Remove Null transition from the NFA and convert it into its equivalent DFA. This is one of the demo files in RegEx, over on GitHub, up to change in notation. If you run the program on it, you’ll get the original 4×4 system, with the 16 linear coefficients and 4 affine coefficients.
I won’t describe how it works since it is well done bitcoin and cryptocurrency trading for beginners audiobook in Raphael’s answer which I suggest to read before. Instead, I focus on in which order you should solve the equations without doing too many extra computations or extra cases. This, and the fact that this is modifying languages more dynamically than the first method make it more error-prone when programming.
The sub-expressions are $AA, AB, ⋯, DC, DD$, as well as $Ya, Yb, Yc, Yd$. If you want to see what the whole thing looks like, without the factoring out of the shared sub-expressions, in-line substitute everything, from top on down. We will use the same example as in Raphael’s answer.
This is the same method as the one described in Raphael’s answer, but from a point of view of a systematic algorithm, and then, indeed, the algorithm. It turns out to be easy and natural to implement once you know where to begin. Also it may be easier by hand if drawing all the automata is impractical for some reason. Step 1 Construct an NFA with Null moves from the given regular expression. Can anyone clear up how to ‘describe each step clearly’? It just seems like a set of basic rules rather than an algorithm with steps to follow.
At first, you can only use the direct transitions. Note that now that the algorithm is written, this is a lot like the transitive closure method. I do not recommend implementing different types of bitcoin wallets that you need to know about 2021 the algorithm, but using the method to do that by hand is a good idea. Please include a general decription of your method as well as a non-trivial example.