Model of computation

In computer science, and more specifically in computability theory and computational complexity theory, a model of computation is a model which describes how an output of a mathematical function is computed given an input. A model describes how units of computations, memories, and communications are organized. The computational complexity of an algorithm can be measured given a model of computation. Using a model allows studying the performance of algorithms independently of the variations that are specific to particular implementations and specific technology.

For computer models simulating complex systems, see Computational model.

Models

Models of computation can be classified in three categories: sequential models, functional models, and concurrent models.

Sequential models include:

• Finite state machines
• Pushdown automata
• Random access machines
• Turing machines

Functional models include:

• Lambda calculus
• General recursive functions
• Combinatory logic
• Abstract rewriting systems

Concurrent models include:

• Cellular automaton
• Kahn process networks
• Petri nets
• Synchronous Data Flow
• Interaction nets
• Actor model

Models differ in their expressive power; for example, each function that can be computed by a Finite state machine can also be computed by a Turing machine, but not vice versa.

A nondeterministic model of computation is associated with some of these models of computation. Nondeterministic models are not useful for practical computation; they are used in the study of computational complexity of algorithms. The unsolved problem P = NP is a well-known example.

Uses

In the field of runtime analysis of algorithms, it is common to specify a computational model in terms of primitive operations allowed which have unit cost, or simply unit-cost operations. A commonly used example is the random access machine, which has unit cost for read and write access to all of its memory cells. In this respect, it differs from the above-mentioned Turing machine model.

Categories

There are many models of computation, differing in the set of admissible operations and their computations cost. They fall into the following broad categories:

• Abstract machine and models equivalent to it (e.g. lambda calculus is equivalent to the Turing machine) - used in proofs of computability and upper bounds on computational complexity of algorithms.
• Decision tree models - used in proofs of lower bounds on computational complexity of algorithmic problems.

See also

• Stack machine (0-operand machine)
• Accumulator machine (1-operand machine)
• Register machine (2,3,... operand machine)
• Random access machine
• Cell-probe model

References

Further reading

• Fernández, Maribel (2009). Models of Computation: An Introduction to Computability Theory. Undergraduate Topics in Computer Science. Springer. ISBN 978-1-84882-433-1.
• Savage, John E. (1998). Models Of Computation: Exploring the Power of Computing. Addison-Wesley. ISBN 978-0201895391.