Model of computation
This article relies largely or entirely on a single source. (February 2021)
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.
Models of computation can be classified into three categories: sequential models, functional models, and concurrent models.
Sequential models include:
- Finite state machines
- Post machines (Post–Turing machines and tag machines).
- Pushdown automata
- Register machines
- Turing machines
Functional models include:
- Abstract rewriting systems
- Combinatory logic
- General recursive functions
- Lambda calculus
- μ-recursive functions
Concurrent models include:
- Actor model
- Cellular automaton
- Interaction nets
- Kahn process networks
- Logic gates and digital circuits
- Petri nets
- Synchronous Data Flow
Some of these models have both deterministic and nondeterministic variants. Nondeterministic models are not useful for practical computation; they are used in the study of computational complexity of algorithms.
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.
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.
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.
- Stack machine (0-operand machine)
- Accumulator machine (1-operand machine)
- Register machine (2,3,... operand machine)
- Random-access machine
- Cell-probe model
- Robertson–Webb query model
- Chomsky hierarchy
- Turing completeness
- "Models of Computation" (PDF).