Answer:
1)
In the context of automata theory, a DFA (Deterministic Finite Automaton) configuration refers to the state of the DFA along with the current input symbol being processed. It represents the instantaneous snapshot of the DFA during its computation.
A DFA configuration consists of two components:
Current State: It represents the state in which the DFA is currently located. In a DFA, the state is an essential part of its definition and determines the behaviour of the automaton.
Remaining Input: It represents the portion of the input yet to be processed by the DFA. As the DFA reads input symbols one by one, the remaining input is reduced until it is completely consumed.
Let's consider a simple example of a DFA that recognizes the language of all binary strings ending with '01'. The DFA has two states: State A and State B. Here's an example of a DFA configuration:
Current State: State B
Remaining Input: 1101
In this example, the DFA is in State B, and the remaining input is '1101'. It indicates that the DFA has already read the input '11' and is currently processing the symbol '0'. Based on the transition rules of the DFA, it will move to another state or remain in the same state, depending on the current state and input symbol.
2)
A DFA (Deterministic Finite Automaton) and an NFA (Nondeterministic Finite Automaton) are both types of finite automata used in automata theory. The main difference between them lies in their behaviour and the nature of transitions between states.
Determinism vs. Nondeterminism:
DFA: A DFA is deterministic, meaning that for any given state and input symbol, there is a unique transition to the next state. It follows a single, well-defined path for each input symbol.
NFA: An NFA is nondeterministic, meaning that for a given state and input symbol, there can be multiple possible transitions leading to different states. It can have several possible paths for each input symbol.
Transition Function:
DFA: In a DFA, the transition function is defined as a mapping from each state and input symbol to a unique next state. It is a total function, ensuring that every state and input symbol has a defined transition.
NFA: In an NFA, the transition function is defined as a mapping from each state and input symbol to a set of possible next states. It allows multiple transitions from the same state with the same input symbol or even transitions with the empty string (ε).
Acceptance of Input:
DFA: In a DFA, acceptance of an input string occurs if, after reading the entire input, the DFA is in an accepting state (a designated final state). If the DFA ends in a non-accepting state, the input is rejected.
NFA: In an NFA, acceptance of an input string can be more flexible. It can accept an input string if there exists at least one possible path through the NFA that leads to an accepting state. It is not necessary for all possible paths to lead to an accepting state.
Memory:
DFA: A DFA has no memory of the input it has previously read. It only considers the current input symbol and the current state to determine the next state.
NFA: An NFA can have memory by using ε-transitions, which allow it to transition to a new state without consuming any input symbol. It can make decisions based on its current state and the remaining input without reading additional input symbols.
Overall, DFAs are simpler and easier to analyze due to their deterministic nature, while NFAs offer more expressive power with their nondeterministic behaviour and ε-transitions. However, it's important to note that both DFA and NFA are equivalent in terms of the languages they can recognize, meaning that for any language recognized by an NFA, there exists an equivalent DFA and vice versa.
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