Finite-State Machines Diagrams and Tables

Questions and Answers

What components are included in a finite-state machine?

A finite set of states, input alphabet, output alphabet, transition function, output function, and an initial state (correct)

A finite set of states and a deterministic output function

A series of inputs and a recursive output function

An initial state and a single transition function

In the context of finite-state machines with output, what does the output function g do?

Initiates the machine from the start state

Generates the output based on state and input pair (correct)

Determines the next state based on the current state

Assigns an input character to each state

Which of the following applications can utilize finite-state machines?

Recognizing speech and spell checking (correct)

Calculating complex mathematical equations

Rendering 3D graphics

Developing neural networks

What is a directed graph with labeled edges used to represent in finite-state machines?

<p>A state diagram of the finite-state machine</p> Signup and view all the answers

Which of the following best describes the transition function f in a finite-state machine?

<p>It determines the next state from the current state and input</p> Signup and view all the answers

Study Notes

Finite-State Machines Overview

Finite-state machines (FSMs) model various machines, especially in computer systems.
Components of FSM include a finite set of states, a starting state, an input alphabet, and a transition function.
FSMs are widely utilized for spell checking, grammar checking, searching text, and speech recognition.

Definition of Finite-State Machines with Output

A finite-state machine M is defined by tuples: M = (S, I, O, f, g, s₀).
- S = finite set of states.
- I = finite input alphabet.
- O = finite output alphabet.
- f = transition function determining next state based on current state and input.
- g = output function producing output based on current state and input.
- s₀ = initial state.

State Table and Diagrams

State tables depict the transition function and output function.
State diagrams are directed graphs where:
- Circles represent states.
- Arrows show transitions labeled with input/output pairs.

Input and Output Relationships

Input strings result in state transitions and produce output strings.
The output function g can be extended to work with input strings, denoting g(x) = y for input x yielding output y.

Example Outputs from FSMs

A specific input string, such as 101011, produces an output string, like 001000.
Each transition through states generates corresponding outputs.

Memory Limitations of FSMs

FSMs have limited memory due to a finite number of states, which restricts their functionality for complex tasks.

Unit-Delay Machine

A finite-state machine can be designed to delay an input string by one unit of time.
This machine utilizes three states to remember the last two inputs, producing an output string that reflects the delayed input.

Error Detection in Strings

FSMs can be designed to detect transmission errors, such as identifying three consecutive 1s in a message.
This type involves:
- A start state (s₀) that remembers when the last bit was not a 1.
- Additional states (s₁ and s₂) to track consecutive 1s.
Inputs of 1 and 0 transition between these states, with outputs responding based on the state of the last three bits.

Description

This quiz focuses on understanding finite-state machines through state diagrams and state tables. Participants will construct state diagrams from given state tables and vice versa. Test your knowledge of these concepts with practical examples and solutions.