Concurrency (computer science)

partial order, without affecting the outcome. This allows for parallel execution of the concurrent units, which can significantly improve overall speed of the execution in multi-processor and multi-core systems. In more technical terms, concurrency refers to the decomposability of a program, algorithm, or problem into order-independent or partially-ordered components or units of computation.^[1]

According to Rob Pike, concurrency is the composition of independently executing computations,^[2] and concurrency is not parallelism: concurrency is about dealing with lots of things at once but parallelism is about doing lots of things at once. Concurrency is about structure, parallelism is about execution, concurrency provides a way to structure a solution to solve a problem that may (but not necessarily) be parallelizable.^[3]

A number of mathematical models have been developed for general concurrent computation including

parallel random-access machine model, the actor model and the Reo Coordination Language

History

distributed systems. Looking back at the origins of the field, what stands out is the fundamental role played by Edsger Dijkstra".^[4]

Issues

Because computations in a concurrent system can interact with each other while being executed, the number of possible execution paths in the system can be extremely large, and the resulting outcome can be

resource starvation.^[5]

Design of concurrent systems often entails finding reliable techniques for coordinating their execution, data exchange,

throughput.^[6]

Theory

Concurrency theory has been an active field of research in theoretical computer science. One of the first proposals was Carl Adam Petri's seminal work on Petri nets in the early 1960s. In the years since, a wide variety of formalisms have been developed for modeling and reasoning about concurrency.

Models

A number of formalisms for modeling and understanding concurrent systems have been developed, including:^[7]

The
parallel random-access machine^[8]

The actor model
Computational bridging models such as the bulk synchronous parallel (BSP) model
Petri nets
Process calculi
- Calculus of communicating systems (CCS)
- Communicating sequential processes (CSP) model
- π-calculus
Tuple spaces, e.g., Linda
Simple Concurrent Object-Oriented Programming (SCOOP)
Reo Coordination Language
Trace monoids

Some of these models of concurrency are primarily intended to support reasoning and specification, while others can be used through the entire development cycle, including design, implementation, proof, testing and simulation of concurrent systems. Some of these are based on message passing, while others have different mechanisms for concurrency.

The proliferation of different models of concurrency has motivated some researchers to develop ways to unify these different theoretical models. For example, Lee and Sangiovanni-Vincentelli have demonstrated that a so-called "tagged-signal" model can be used to provide a common framework for defining the denotational semantics of a variety of different models of concurrency,^[9] while Nielsen, Sassone, and Winskel have demonstrated that category theory can be used to provide a similar unified understanding of different models.^[10]

The Concurrency Representation Theorem in the actor model provides a fairly general way to represent concurrent systems that are closed in the sense that they do not receive communications from outside. (Other concurrency systems, e.g.,

process calculi can be modeled in the actor model using a two-phase commit protocol.^[11]) The mathematical denotation denoted by a closed system S is constructed increasingly better approximations from an initial behavior called ⊥_S using a behavior approximating function progression_S to construct a denotation (meaning ) for S as follows:^[12]

Denote_S ≡ ⊔_i∈ω progression_Sⁱ(⊥_S)

In this way, S can be mathematically characterized in terms of all its possible behaviors.

Logics

Various types of temporal logic^[13] can be used to help reason about concurrent systems. Some of these logics, such as linear temporal logic and computation tree logic, allow assertions to be made about the sequences of states that a concurrent system can pass through. Others, such as action computational tree logic, Hennessy–Milner logic, and Lamport's temporal logic of actions, build their assertions from sequences of actions (changes in state). The principal application of these logics is in writing specifications for concurrent systems.^[5]