Finite State Machines
Introduction
A Finite State Machine (FSM) is a mathematical model of computation used to design both computer programs and sequential logic circuits. It is conceived as an abstract machine that can be in one of a finite number of states. The machine is only in one state at a time; the state it is in at any given time is called the current state. It can change from one state to another when initiated by a triggering event or condition, this is called a transition.
Definition
A Finite State Machine is defined by a list of its states, its initial state, and the conditions for each transition. FSMs are of two types: acceptors or recognizers; and transducers. Acceptors have a boolean end state (accept or reject) and produce a binary output, they are used as control circuits. Transducers produce an output based on given inputs and are used in algorithmic applications.
Components of a Finite State Machine
Finite State Machines have five parts:
1. A finite set of states (Q) 2. A finite set of input symbols (Σ) 3. A finite set of output symbols (Γ) 4. A transition function (δ) 5. An initial state (q0)
Types of Finite State Machines
There are two types of FSMs: Mealy Machines and Moore Machines.
Mealy Machine
A Mealy Machine is a FSM whose output values are determined both by its current state and the current inputs. This is in contrast to a Moore Machine, whose (Moore) output values are determined solely by its current state.
Moore Machine
A Moore Machine is a FSM whose output values are determined solely by its current state. This is in contrast to a Mealy Machine, whose (Mealy) output values are determined both by its current state and the current inputs.
Applications of Finite State Machines
FSMs have numerous applications in computer science, linguistics, artificial intelligence, systems biology, bioinformatics, and computer hardware, among others.
In Computer Science
In computer science, finite state machines are widely used in modeling of application behavior, design of hardware digital systems, software engineering, compilers, network protocols, and the study of computation and languages.
In Linguistics
In Computational Linguistics, finite state machines are used in the computational models of natural language grammars and languages.
In Artificial Intelligence
In artificial intelligence, finite state machines are used to model the behavior of entities such as software agents or robots, allowing a simple way to provide a "brain" for a software or robotic entity.
In Systems Biology and Bioinformatics
In systems biology and bioinformatics, finite state machines are used to model and simulate genetic networks and biochemical pathways.
In Computer Hardware
In computer hardware, finite state machines are used in the design of digital circuits for sequential logic, such as computer memory and CPUs.
Advantages and Disadvantages of Finite State Machines
Like any other model, finite state machines have their advantages and disadvantages.
Advantages
1. Simplicity: FSMs are simple and intuitive. They provide a clear, visual representation of control flow. 2. Modularity: FSMs can be easily composed with other FSMs to create more complex behavior. 3. Predictability: FSMs have a predictable and deterministic behavior.
Disadvantages
1. State Explosion: For complex systems, the number of states in an FSM can grow exponentially, leading to unmanageable state complexity. 2. Lack of Flexibility: FSMs are not suitable for systems where the number of states is dynamic or not known in advance.
Conclusion
Finite State Machines are a fundamental concept in computer science and have a wide range of applications. Despite their limitations, they are a powerful tool for modeling and understanding complex systems.