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Liminf progress measures

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Mathematical Foundations of Programming Semantics (MFPS 1991)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 598))

Abstract

Consider a program P that satisfies a specification S. It is natural to think that every single step of a computation of P somehow contributes to making the computation closer to satisfying S. For specifications that define liveness properties, methods that directly quantify such a notion of progress or convergence are often quite limited in scope. Instead many approaches, such as those that deal with termination under fairness, rely on program transformations, since there was no known way of directly expressing progress towards fair termination.

In this article we use the novel concept of progress measures to quantify progress for a large class of specifications. The main result is a precise characterization of what it means for a program to satisfy a Liminf specification. Such specifications define properties at a higher level of the Borel hierarchy than earlier methods based on Büchi automata and Propositional Temporal Logic. In particular, we give a solution to the problem of verification involving the very general notion of extreme fairness. More generally, our results establish a connection between assertional reasoning about programs and descriptive set theory.

This work was mainly carried out at Cornell University and supported by grants from the University of Aarhus, Denmark; Forskerakademiet, Aarhus; and the Thanks to Scandinavia Foundation Inc., NY.

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Author notes

  1. Nils Klarlund

    Present address: Department of Computer Science, Aarhus University, Ny Munkegade, DK-8000, Aarhus C

Authors and Affiliations

  1. IBM T.J. Watson Research Center, PO BOX 704, 10598, Yorktown Heights, NY

    Nils Klarlund

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  1. Nils Klarlund
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Stephen Brookes Michael Main Austin Melton Michael Mislove David Schmidt

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© 1992 Springer-Verlag Berlin Heidelberg

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Klarlund, N. (1992). Liminf progress measures. In: Brookes, S., Main, M., Melton, A., Mislove, M., Schmidt, D. (eds) Mathematical Foundations of Programming Semantics. MFPS 1991. Lecture Notes in Computer Science, vol 598. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55511-0_25

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  • DOI: https://doi.org/10.1007/3-540-55511-0_25

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55511-7

  • Online ISBN: 978-3-540-47194-3

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