Computer Science – Logic in Computer Science
Scientific paper
2011-05-31
LMCS 7 (3:4) 2011
Computer Science
Logic in Computer Science
43 pages
Scientific paper
10.2168/LMCS-7(3:4)2011
Size-Change Termination (SCT) is a method of proving program termination based on the impossibility of infinite descent. To this end we use a program abstraction in which transitions are described by Monotonicity Constraints over (abstract) variables. When only constraints of the form x>y' and x\geq y' are allowed, we have size-change graphs. In the last decade, both theory and practice have evolved significantly in this restricted framework. The crucial underlying assumption of most of the past work is that the domain of the variables is well-founded. In a recent paper I showed how to extend and adapt some theory from the domain of size-change graphs to general monotonicity constraints, thus complementing previous work, but remaining in the realm of well-founded domains. However, monotonicity constraints are, interestingly, capable of proving termination also in the integer domain, which is not well-founded. The purpose of this paper is to explore the application of monotonicity constraints in this domain. We lay the necessary theoretical foundation, and present precise decision procedures for termination; finally, we provide a procedure to construct explicit global ranking functions from monotonicity constraints in singly-exponential time, and of optimal worst-case size and dimension (ordinal).
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