Finite State Machines and Automata Theory with JFLAP

Fundamentals of Abstract Machines

An abstract machine is a model in computer science representing a digital, discrete-time host. The simplification of complex skills makes it easier to understand the behavior of a machine and compare different models.

Core Behavior and State Transitions

The basic behavior of an automaton remains consistent: the machine processes an external command sequence of characters. The machine exists in a specific state. Each time an input character arrives, the machine moves to a successor state based on the current state and the input. This process is known as a state transition.

The set of possible transitions defines the machine's behavior. These are described using a transition function, which dictates how the machine moves from one state to another. In diagrams, these transitions are represented as arrows connecting states.

Key Components of an Automaton

• Current State (q): The specific state the machine occupies at any given time.
• Start State: Indicated by an arrow labeled Start.
• Final State: Represented by a double circle. A machine can have several final states.
• Input Alphabet: The set of characters, words, or symbols that the machine is designed to process.

Input Processing and Language Acceptance

An automaton considers individual actions in a sequence and reacts accordingly. While theoretical models use numbers or letters, real-world machines might use buttons or coins. A word is a string consisting of characters from the alphabet.

The automaton accepts an input word if, and only if, it is in a final state after reading the entire sequence. Otherwise, the automaton rejects the input word. The collection of all words accepted by the machine is called its language.

Binary System Representation

Automata often process binary data. For example, the binary number 11011 is calculated as follows:

1*2^0 + 1*2^1 + 0*2^2 + 1*2^3 + 1*2^4 = 1 + 2 + 0 + 8 + 16 = 27

Creating Automata with JFLAP

JFLAP is a tool used for the automatic creation and simulation of automata models.

Managing States and Transitions

• Adding States: Select the State Creator mode (circle button). You can then place as many states as needed with a mouse click.
• Creating Transitions: Select the Transition mode (arrow button). Connect the corresponding states by clicking on the source state and dragging the mouse to the destination state. You can also create a transition from a state to itself.
• Deleting Elements: Select the Delete mode (skull button). You can then click on the states or transitions you wish to remove.
• Editing States: Right-click on a state to open a context menu. From this menu, you can set a state as Initial or Final.
• Saving Models: Use the File > Save As... menu option to save your work.