All the images above were generated using an online tool for automatically converting regular expressions to non-deterministic finite automata. You can find its source code for the Thompson-McNaughton-Yamada Construction algorithm online. This method is easy to write in a form of an algorithm, but generates absurdly large regular expressions and is impractical if you do it by hand, mostly because this is too systematic. It is a good and simple solution for an algorithm though. There are several methods to do the conversion from finite automata to regular expressions.
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.
The nicest method I have seen is one that expresses the automaton as equation system of (regular) languages which can be solved. It is in particular nice as it seems to yield more concise expressions than other methods. In NDFA, for a particular input symbol, the machine can move to any combination of the states in the machine. In other words, the exact state to which the machine moves cannot be determined. As it has finite number of states, the machine is called Non-deterministic Finite Machine or Non-deterministic Finite Automaton.
I won’t describe how it works since it is well done 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.
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.
You 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 how to buy ever grow coin 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.
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 what is a white-label broker in forex if it may seems a system of equations that seems too symbolic for an algorithm, this one is well-suited for an implementation.
Here I will describe the one usually taught how to buy bitcoin in 7 steps 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 $q$.