NDLI: Ranking functions for size-change termination

Content Provider	ACM Digital Library
Author	Lee, Chin Soon
Copyright Year	2009
Abstract	This article explains how to construct a ranking function for any program that is proved terminating by size-change analysis. The “principle of size-change termination” for a first-order functional language with well-ordered data is intuitive: A program terminates on all inputs, if every infinite call sequence (following program control flow) would imply an infinite descent in some data values. Size-change analysis is based on information associated with the subject program's call-sites. This information indicates, for each call-site, strict or weak data decreases observed as a computation traverses the call-site. The set $\textit{DESC}$ of call-site sequences for which the size-changes imply infinite descent is ω-regular, as is the set $\textit{FLOW}$ of infinite call-site sequences following the program flowchart. If $\textit{FLOW}$ ⊆ $\textit{DESC}$ (a decidable problem), every infinite call sequence would imply infinite descent in a well-ordering—an impossibility—so the program must terminate. This analysis accounts for termination arguments applicable to different call-site sequences, without indicating a ranking function for the program's termination. In this article, it is explained how one can be constructed whenever size-change analysis succeeds. The constructed function has an unexpectedly simple form; it is expressed using only min, max, and lexicographic tuples of parameters and constants. In principle, such functions can be tested to determine whether size-change analysis will be successful. As a corollary, if a program verified as terminating performs only multiply recursive operations, the function that it computes is multiply recursive. The ranking function construction is connected with the determinization of the Büchi automaton for $\textit{DESC}.$ While the result is not practical, it is of value in addressing the scope of size-change reasoning. This reasoning has been applied broadly, in the analysis of functional and logic programs, as well as term rewrite systems.
Starting Page	1
Ending Page	42
Page Count	42
File Format	PDF
ISSN	01640925
e-ISSN	15584593
DOI	10.1145/1498926.1498928
Volume Number	31
Issue Number	3
Journal	ACM Transactions on Programming Languages and Systems (TOPLAS)
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2009-04-21
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	ω-Automaton Determinization Multiple recursion Ranking function Size-change termination Termination analysis
Content Type	Text
Resource Type	Article
Subject	Software

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