, COS4861 Assignment 2 (COMPLETE ANSWERS)
Semester 1 2025 – DUE 2025; 100% correct solutions and
explanations.
QUESTION 1
1.1 Define a Deterministic Finite State Automata (DFSA). Explain
its key components and how it operates with an example.
A Deterministic Finite State Automaton (DFSA) is a mathematical
model of computation used to recognize patterns within input data. It
consists of a finite number of states and transitions between those states
based on input symbols. In a DFSA, for every state and input symbol,
there is exactly one transition to a next state. This determinism ensures
predictable behavior for any given input.
Key Components of a DFSA:
A DFSA is formally defined as a 5-tuple:
M = (Q, Σ, δ, q₀, F) where:
Q is a finite set of states.
Σ is a finite set called the input alphabet.
δ is the transition function, δ: Q × Σ → Q.
q₀ ∈ Q is the initial/start state.
F ⊆ Q is the set of accepting (final) states.
How it operates:
1. The automaton starts in the initial state (q₀).
2. It reads an input symbol and follows the transition defined by δ.
3. It continues processing input symbols, transitioning from state to
state.
4. If the automaton ends in a final state after reading the entire input,
the input is accepted; otherwise, it is rejected.
Semester 1 2025 – DUE 2025; 100% correct solutions and
explanations.
QUESTION 1
1.1 Define a Deterministic Finite State Automata (DFSA). Explain
its key components and how it operates with an example.
A Deterministic Finite State Automaton (DFSA) is a mathematical
model of computation used to recognize patterns within input data. It
consists of a finite number of states and transitions between those states
based on input symbols. In a DFSA, for every state and input symbol,
there is exactly one transition to a next state. This determinism ensures
predictable behavior for any given input.
Key Components of a DFSA:
A DFSA is formally defined as a 5-tuple:
M = (Q, Σ, δ, q₀, F) where:
Q is a finite set of states.
Σ is a finite set called the input alphabet.
δ is the transition function, δ: Q × Σ → Q.
q₀ ∈ Q is the initial/start state.
F ⊆ Q is the set of accepting (final) states.
How it operates:
1. The automaton starts in the initial state (q₀).
2. It reads an input symbol and follows the transition defined by δ.
3. It continues processing input symbols, transitioning from state to
state.
4. If the automaton ends in a final state after reading the entire input,
the input is accepted; otherwise, it is rejected.
