How many final state in dfa

Compiler Design. Computer Organization. Discrete Mathematics. Ethical Hacking. Computer Graphics. Software Engineering. Web Technology. Cyber Security. C Programming. Control System. Data Mining. Data Warehouse. So, a nondeterministic finite automaton can very well work with just one final state. However, if you explode a nondeterministic finite automaton into a deterministic finite automaton, you'll find that you no longer can have epsilon transitions.

The states of the exploded deterministic finite automaton correspond to sets of states in the nondeterministic finite automaton. You will find that you need to mark a state as "final state" if at least one of the NFA states in the set is the final state. There may be multiple such states.

So, in summary: an NFA can very well work with just one final state. Let me provide a characterization of what languages DFAs with a single accepting state can accept. A prefix code is a set of words, none of which is a prefix of another one. It is regular if as a language it is regular. Thus the minimal DFA contains a unique accepting state. Finally, let us show that the decomposition is unique.

From Myhill—Nerode theory, it is known that the minimal number of accepting states equals the number of Myhill—Nerode equivalence classes of words in the language. With some work, it should be possible to identify a combinatorial parameter which determines the minimal number of accepting states in any finite language. Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group.

Create a free Team What is Teams? Learn more. For example, the previous figure has 4 states, state 1 is the start state, and state 4 is the only final state. A DFA accepts a string if starting from the start state and moving from state to state, each time following the arrow that corresponds the current input character, it reaches a final state when the entire input string is consumed.

Context free languages can be recognized by pushdown automata. Regular languages can be recognized by finite automata. Pushdown Automata is a finite automata with extra memory called stack which helps Pushdown automata to recognize Context Free Languages. A pushdown automaton reads a given input string from left to right.

In each step, it chooses a transition by indexing a table by input symbol, current state, and the symbol at the top of the stack. A pushdown automaton can also manipulate the stack, as part of performing a transition. In final state acceptability, a PDA accepts a string when, after reading the entire string, the PDA is in a final state.

From the starting state, we can make moves that end up in a final state with any stack values. The non-deterministic pushdown automata is very much similar to NFA. Every regular language is accepted by some PDA basically, just ignore the stack… Idea: on input w, M nondeterministically picks a leftmost derivation of w from S.

Begin typing your search term above and press enter to search. Press ESC to cancel. Ben Davis May 31, How many states can a DFA have?