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erotavlas
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Taking a regular expression and converting it to a DFA with transition table, can you go backwards? I.e. take one of the rows of the table and determine what input string would be accepted for that row?
Fooality said:So you want to enumerate the strings a finite automata matches? Intuitively that should be pretty simple. Of course that set is often infinite, and you get into issues of enumerating infinite sets, but the set should be countably infinite, so it can be done. Do I understand you right?
Fooality said:well, its good to visualize the Finite Automaton in terms of a state diagram: labelled circles (s1, s2, ...) connected by arrows representing state transitions, ending either in accept state or reject state. To enumerate all the accepted strings we want a function that walks through each state, forking as needed, and returning on accept. So for regex 'abc' it walks through 4 states a,b,c,accept and outputs on accept. For one like 'a(b|d)c+e' the function will fork for the OR state once, and for infinitely for c+ state. So its a recursive function. Of course you can pass a variable for recursion depth to limit string length.
Unless I am missing something big, that should work it seems.
A DFA (Deterministic Finite Automaton) transition table is a table that represents the states and transitions of a DFA. It shows all possible combinations of states and inputs, along with the corresponding next state for each combination.
Yes, a string can be obtained from a DFA transition table by following the transitions from the initial state to the final state, based on the inputs given in the string. If the final state is an accepting state, then the string is accepted by the DFA.
To read a DFA transition table, start at the initial state and follow the transitions based on the inputs given in the string. Each row represents a state, and each column represents an input symbol. The value in each cell represents the next state that the DFA will transition to when that input is given in that state. Keep following the transitions until you reach the final state.
Yes, a DFA transition table can determine if a string is valid by following the transitions from the initial state to the final state, based on the inputs given in the string. If the final state is an accepting state, then the string is considered valid. If the final state is not an accepting state, then the string is considered invalid.
A DFA transition table is created by identifying all possible states of the DFA and all possible inputs. Then, for each state and input combination, the next state is determined based on the transition rules of the DFA. This information is then organized into a table format, with rows representing states and columns representing inputs, to create the DFA transition table.