# 1. Objective / Мета роботи

**Design and implement a finite state machine that scans a string and extracts
numbers from it, in four stages of increasing capability.**

By the end of the work the student should be able to:

- describe a **finite state machine** by its **states**, input **alphabet**,
  **transition** rules, start state, and accepting states;
- scan a string **character by character**, classifying each character and driving
  the machine's state;
- recognise, in growing order of difficulty, **all digits**, **all integers**,
  **all positive rational numbers**, and **all (signed) rational numbers** in a
  string;
- express the scanner as a **transition table** or **state diagram** and translate
  it into code;
- reason about the scanner's **linear** time complexity in the length of the input.

The work connects the abstract model of automata to a concrete, everyday task —
tokenising text — and lays the groundwork for lexical analysis in compilers.