# Finite State Machines (FSMs) without Output

**Overview of Finite State Machines (FSMs) Without Output**

- A
**finite state machine (FSM)**is a mathematical model of computation used to simulate sequential logic, algorithms, and operations in computer science and various digital systems. - An FSM without output, also called a
**deterministic finite automaton (DFA)**, consists of a**set of states**, a**set of input symbols**, a**transition function**that takes a state and an input symbol and produces the next state, and a**start state**. - The DFA continues to change states based on the input and transition function until all inputs have been consumed.

**Defining Elements of Finite State Machines**

**States**: These are conditions that our machine can be in. It is termed**finite**because the machine has a limited or finite number of states.**Input Symbols**: These are triggers or information that the machine reads and responds to by transitioning from one state to another.**Transition Function**: This is a rule or set of rules that determine the next state based on the current state and the input symbol.**Start State**: This is the state where any input is processed initially.

**Underlying Concepts of FSMs Without Output**

- In an FSM, the same input can lead to different outputs depending on the current state, hence giving rise to the concept of
**state-dependent behaviour**. - An important characteristic of a DFA is
**determinism**. It means for each state and input symbol, there is one and only one transition. - FSMs are called
**memoryless**as they do not possess any memory and the operational decision is determined solely based on the present state and input, not on the sequence of past inputs.

**Applications of FSMs Without Output**

- FSMs are used in the design of digital systems and algorithms where sequential or state-dependent behaviour is needed.
- In computer science, FSMs have a wide range of uses including in parsing (syntax analysis), text processing, and protocol design among others.
- FSMs are pivotal in compiler construction where it helps to convert high-level code into machine-readable form.

**Understanding FSMs in the Theory of Computation**

- In
**theory of computation**, FSMs play a critical role in understanding and modeling computation, algorithms, and problems. - It serves as a simple model to understand computational processes and capable of replicating the computational power of a computer with unlimited memory.
- While relatively simple, FSMs provide significant insights into
**fundamental properties of computation**, and are a cornerstone of study in courses covering computation theory, computer science, and digital systems design.

In summary, FSMs without output provide a base level understanding of automata used to model computation in computer science. Understanding FSMs is fundamental to understanding more complex topics like Turing machines and computational complexity.