Abstract
Here we look at shared variables in depth, including a study of dirty variables via the bakery algorithm and Simpson’s 4-slot algorithm (where we propose a version that avoids known difficulties arising from dirty flag variables). We also define what it means for one shared variable program to refine another one, and introduce various ideas necessary to create finite model-checked proofs of programs (such as the bakery algorithm) that involve unbounded integer types.
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Notes
- 1.
We have already seen one mutual exclusion algorithm, namely the bakery algorithm, in which no location is written by more than one thread. A second is Knuth’s algorithm [77], an implementation of which can be found with the examples accompanying this chapter.
- 2.
In the theory of concurrent algorithms, researchers sometimes consider a parallel machine model in which multiple processors are allowed to make simultaneous writes to the same location, but only if all the written values are the same: a Parallel Random Access Machine with Common Concurrent Writes, see [39].
- 3.
Note that this, and the earlier checks in this section, resemble the check for a data-independent process being a buffer described on p. 406.
- 4.
It is legitimate to make clean writes to locations such as this and okread[i] that are shared between threads and introduced by us for specification purposes, because they are not part of the algorithm itself, merely tools to help us observe it.
- 5.
This type of context also applies to any case where there is no parallelism in the complete system.
- 6.
In the case of integer locations we only consider the case of writes of values within the content type of the given location, since, thanks to our error regime, no thread will attempt any other write.
- 7.
refsva.csp does not disable the other functions of svacomp.csp, and in fact the parser in SVA’s front end always uses the combination of these two files, even when no refinement between SVL terms is tested.
- 8.
Furthermore, this replacement only created a problem with at least 5 threads.
- 9.
Another, seemingly more efficient, way of achieving this effect is set out on p. 472.
- 10.
Indeed, it is practically better to have all three of these slots replaced by a single one randi representing a random value. The most efficient way to achieve a random value is to make a variable such as randi or randb writable by the external environment. See the example scripts.
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Roscoe, A.W. (2010). Understanding Shared-Variable Concurrency. In: Understanding Concurrent Systems. Texts in Computer Science. Springer, London. https://doi.org/10.1007/978-1-84882-258-0_19
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DOI: https://doi.org/10.1007/978-1-84882-258-0_19
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