A concurrent object is a data object shared by concurrent processes. Linearizability is a correctness condition for concurrent objects that exploits the semantics of abstract data types. It permits a high degree of concurrency, yet it permits programmers to specify and reason about concurrent objects using known techniques from the sequential domain. Linearizability provides the illusion that each operation applied by concurrent processes takes effect instantaneously at some point between its invocation and its response, implying that the meaning of a concurrent object's operations can be given by pre- and post-conditions. This paper defines linearizability, compares it to other correctness conditions, presents and demonstrates a method for proving the correctness of implementations, and shows how to reason about concurrent objects, given they are linearizable.

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Linearizability: a correctness condition for concurrent objects

From the Publisher:
Since the introduction of Hoares' Communicating Sequential Processes notation, powerful new tools have transformed CSP into a practical way of describing industrial-sized problems. This book gives you the fundamental grasp of CSP concepts you'll need to take advantage of those tools.Part I provides a detailed foundation for working with CSP, using as little mathematics as possible. It introduces the ideas behind operational, denotational and algebraic models of CSP. Parts II and III go into greater detail about theory and practice. Topics include: parallel operators, hiding and renaming, piping and enslavement, buffers and communication, termination and sequencing, and semantic theory. Three detailed practical case studies are also presented.For anyone interested in modeling sequential processes.

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The Theory and Practice of Concurrency

LOTOS is a specification language that has been specifically developed for the formal description of the OSI (Open Systems Interconnection) architecture, although it is applicable to distributed, concurrent systems in general. In LOTOS a system is seen as a set of processes which interact and exchange data with each other and with their environment. LOTOS is expected to become an ISO international standard by 1988.

https://ris.utwente.nl/ws/files/6793455/Bolognesi87introduction.pdf

Introduction to the ISO specification language LOTOS

As software systems become more complex, the overall system structure—or software architecture—becomes a central design problem. An important step toward an engineering discipline of software is a formal basis for describing and analyzing these designs. In the article we present a formal approach to one aspect of architectural design: the interactions among components. The key idea is to define architectural connectors as explicit semantic entities. These are specified as a collection of protocols that characterize each of the participant roles in an interaction and how these roles interact. We illustrate how this scheme can be used to define a variety of common architectural connectors. We further provide a formal semantics and show how this leads to a system in which architectural compatibility can be checked in a way analogous to type-checking in programming languages.

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A formal basis for architectural connection

Testing equivalences for processes

A mathematical model for communicating sequential processes is given, and a number of its interesting and useful properties are stated and proved. The possibilities of nondetermimsm are fully taken into account.

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A Theory of Communicating Sequential Processes

http://www0.cs.ucl.ac.uk/staff/p.ohearn/papers/brookes_concur04.pdf

A semantics for concurrent separation logic

We extend the failures model of communicating processes to allow a more satisfactory treatment of divergence in addition to deadlock. The relationship between the revised model and the old model is discussed, and we make some connections with various models proposed by other authors.

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An Improved Failures Model for Communicating Processes

Gives a new denotational semantics for a shared variable parallel programming language and proves full abstraction. The semantics gives identical meanings to commands if and only if they induce the same partial correctness behavior in all program contexts. The meaning of a command is a set of transition traces, which record the ways in which a command may interact with and be affected by its environment. It is shown how to modify the semantics to incorporate new program constructs, to allow for different levels of granularity or atomicity, and to model fair infinite computation, in each case achieving full abstraction with respect to an appropriate notion of program behavior. >

/pdf/full-abstraction-for-a-shared-variable-parallel-language-2vz8kelkzz.pdf

Full abstraction for a shared variable parallel language

We present a denotational semantics based on action traces, for parallel programs which share mutable data and synchronize using resources and conditional critical regions. We introduce a resource-sensitive logic for partial correctness, adapting separation logic to the concurrent setting, as proposed by O'Hearn. The logic allows program proofs in which ownership of a piece of state is deemed to transfer dynamically between processes and resources. We prove soundness of this logic, using a novel local interpretation of traces, and we show that every provable program is race-free.

Stephen Brookes

Papers

A Theory of Communicating Sequential Processes

A semantics for concurrent separation logic

An Improved Failures Model for Communicating Processes

Full abstraction for a shared variable parallel language

A semantics for concurrent separation logic