Size-Change termination analysis in k-bits

Authors:
Michael Codish;Vitaly Lagoon;Peter Schachte;Peter J. Stuckey
Affiliations:
Department of Computer Science, Ben-Gurion University, Israel;Department of Computer Science and Software Engineering, The University of Melbourne, Australia;Department of Computer Science and Software Engineering, The University of Melbourne, Australia;Department of Computer Science and Software Engineering, The University of Melbourne, Australia
Venue:
ESOP'06 Proceedings of the 15th European conference on Programming Languages and Systems
Year:
2006

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Abstract

Size-change termination analysis is a simple and powerful technique successfully applied for a variety of programming paradigms. A main advantage is that termination for size-change graphs is decidable and based on simple linear ranking functions. A main disadvantage is that the size-change termination problem is PSPACE-complete. Proving size change termination may have to consider exponentially many size change graphs. This paper is concerned with the representation of large sets of size-change graphs. The approach is constraint based and the novelty is that sets of size-change graphs are represented as disjunctions of size-change constraints. A constraint solver to facilitate size-change termination analysis is obtained by interpreting size-change constraints over a sufficiently large but finite non-negative integer domain. A Boolean k-bit modeling of size change graphs using binary decision diagrams leads to a concise representation. Experimental evaluation indicates that the 2-bit representation facilitates an efficient implementation which is guaranteed complete for our entire benchmark suite.