Finite-State Machines Diagrams and Tables

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.

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.