COS4861 Assignment 2 (QUALITY ANSWERS) 2025

COS4861
Assignment 2

2025

, Question 1.1: Definition of Deterministic Finite State Automaton (DFSA)

[10 Marks]

A Deterministic Finite State Automaton (DFSA) is a fundamental computational model
used to determine whether a given string belongs to a particular regular language. It
functions by processing an input string symbol by symbol, following well-defined
transitions between states.

A DFSA is formally described as a 5-tuple:

 Q: A finite set of states

 Σ: A finite input alphabet

 δ: A transition function defined as δ: Q × Σ → Q

 q₀: The start state (an element of Q)

 F: A set of accept states (F is a subset of Q)

In a DFSA, every state and input symbol has exactly one defined transition (i.e., it is
deterministic).

Example:

Let the DFSA be defined as M = (Q, Σ, δ, q₀, F), where:

 Q = {q₀, q₁}

 Σ = {0, 1}

 q₀ is the start state

 F = {q₁} (final state)

 δ is defined as:

o δ(q₀, 0) = q₀

o δ(q₀, 1) = q₁

o δ(q₁, 0) = q₀