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SAT-based termination analysis using monotonicity constraints over the integers

Published online by Cambridge University Press:  06 July 2011

MICHAEL CODISH ,
IGOR GONOPOLSKIY ,
AMIR M. BEN-AMRAM ,
CARSTEN FUHS  and
JÜRGEN GIESL
MICHAEL CODISH
Affiliation:
Department of Computer Science, Ben-Gurion University, Israel (e-mail: mcodish@cs.bgu.ac.il, gonopols@cs.bgu.ac.il)
IGOR GONOPOLSKIY
Affiliation:
Department of Computer Science, Ben-Gurion University, Israel (e-mail: mcodish@cs.bgu.ac.il, gonopols@cs.bgu.ac.il)
AMIR M. BEN-AMRAM
Affiliation:
School of Computer Science, Tel-Aviv Academic College, Israel (e-mail: amirben@mta.ac.il)
CARSTEN FUHS
Affiliation:
LuFG Informatik 2, RWTH Aachen University, Germany (e-mail: fuhs@informatik.rwth-aachen.de, giesl@informatik.rwth-aachen.de)
JÜRGEN GIESL
Affiliation:
LuFG Informatik 2, RWTH Aachen University, Germany (e-mail: fuhs@informatik.rwth-aachen.de, giesl@informatik.rwth-aachen.de)
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Abstract

We describe an algorithm for proving termination of programs abstracted to systems of monotonicity constraints in the integer domain. Monotonicity constraints are a nontrivial extension of the well-known size-change termination method. While deciding termination for systems of monotonicity constraints is PSPACE complete, we focus on a well-defined and significant subset, which we call MCNP (for “monotonicity constraints in NP”), designed to be amenable to a SAT-based solution. Our technique is based on the search for a special type of ranking function defined in terms of bounded differences between multisets of integer values. We describe the application of our approach as the back end for the termination analysis of Java Bytecode. At the front end, systems of monotonicity constraints are obtained by abstracting information, using two different termination analyzers: AProVE and COSTA. Preliminary results reveal that our approach provides a good trade-off between precision and cost of analysis.

Keywords

termination analysismonotonicity constraintsSAT encoding
Type
Regular Papers
Information
Theory and Practice of Logic Programming , Volume 11 , Special Issue 4-5: 27th International Conference on Logic Programming , July 2011 , pp. 503 - 520
Copyright
Copyright © Cambridge University Press 2011

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