Model of computation

Model of Computation is a formal framework used in Computer Science and Mathematics to describe the computational abilities of a machine. It is a theoretical construct that defines the rules of computation, including the set of allowable operations, the format and type of inputs and outputs, and the speed or cost of operations.

Definition

A Model of Computation consists of three main components:

1. States: These are the configurations that a machine can be in. For example, in a Turing machine, the state includes the current position of the head, the current state of the machine, and the contents of the tape.
2. Transitions: These are the rules that determine how the machine moves from one state to another. In a Turing machine, the transition function takes the current state and the current tape symbol as input and outputs the new state, the new tape symbol, and the direction in which to move the head.
3. Start and Accept States: The start state is the state in which the machine begins its computation. The accept states (also known as final or halting states) are the states in which the machine can halt and accept the input.

Types of Models of Computation

There are several types of models of computation, each with its own strengths and weaknesses. Some of the most common include:

1. Turing Machines: These are the most powerful model of computation, capable of simulating any other model. They are used as the standard against which other models are compared.
2. Finite Automata: These are the simplest model of computation, capable of recognizing regular languages.
3. Pushdown Automata: These are more powerful than finite automata, capable of recognizing context-free languages.
4. Random Access Machines: These are a model of computation that more closely resembles modern computers, with random access memory and a set of basic operations.

Complexity Theory

In Complexity Theory, models of computation are used to classify problems based on their computational complexity. The most well-known complexity classes, P and NP, are defined in terms of a deterministic Turing machine and a non-deterministic Turing machine, respectively.

See Also

• Computational Model
• Church-Turing Thesis
• Computational Complexity Theory
• Automata Theory

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