Design a pushdown automata for the same.
Otherwise, you can use the following grammer :
S -> aSb|bSa|<NULL>
Finite automata with ε-moves, also known as epsilon transitions, are a type of finite state machine that allows transitions between states without consuming any input symbols. This means that the automaton can move from one state to another spontaneously, enabling it to represent a broader range of languages than standard finite automata. Epsilon transitions can simplify the design of automata, particularly when converting from nondeterministic finite automata (NFA) to deterministic finite automata (DFA) or when constructing automata for regular expressions.
single possible output for a given input
Finite automata are machines used to recognize patterns from input set of characters. They either reject or accept inputs based on the already defined pattern set by the FA.
The union of two deterministic finite automata (DFA) can be achieved by creating a new DFA that combines the states and transitions of the original DFAs. This new DFA will accept a string if either of the original DFAs would accept that string.
DFA - deterministic finite automata NFA - non-deterministic finite automata
A deterministic Finite Automata)DFA will have a single possible output for a given input.The answer is deterministic because you can always feel what the output will be.A (Nondeterministic Finite Automata)NFA will have at least one input which will cause a "choice" to be made during a state transition,unlike a (deterministic Finite Automata)DFA one input can cause multiple outputs for a given (Nondeterministic Finite Automata)NFA.
No, not all deterministic finite automata (DFAs) are also non-deterministic finite automata (NFAs). DFAs have a single unique transition for each input symbol, while NFAs can have multiple transitions for the same input symbol.
Yes, it is possible to show that all deterministic finite automata (DFA) are decidable.
finite automata
Deterministic finite state automata
DFA - Deterministic Finite Automata NFA - Non-Deterministic Finite Automata Both DFAs and NFAs are abstract machines which can be used to describe languages.
The DFA for the empty set in automata theory is significant because it represents a finite automaton that cannot accept any input strings. This helps in understanding the concept of unreachable states and the importance of having at least one accepting state in a deterministic finite automaton.