Abstract
We show how to view computations involving very general liveness properties as limits of finite approximations. This computational model does not require introduction of infinite nondeterminism as with most traditional approaches. Our results allow us directly to relate finite computations in order to infer properties about infinite computations. Thus we are able to provide a mathematical understanding of what simulations and bisimulations are when liveness is involved.
In addition, we establish links between verification theory and classical results in descriptive set theory. Our result on simulations is the essential contents of the Kleene-Suslin Theorem, and our result on bisimulation expresses Martin’s Theorem about the determinacy of Borel games.
This article is a revised and extended version of an earlier technical report (“Convergence Measures,” TR90-1106, Cornell University), which was extracted from the author’s Ph.D. thesis. Due to space limitations, all proofs have been omitted in this article.
Partially supported by an Alice & Richard Netter Scholarship of the Thanks to Scandinavia Foundation, Inc. and NSF grant CCR 88-06979.
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Klarlund, N. (1994). The Limit View of Infinite Computations. In: Jonsson, B., Parrow, J. (eds) CONCUR ’94: Concurrency Theory. CONCUR 1994. Lecture Notes in Computer Science, vol 836. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-48654-1_27
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