The size-change principle for program termination
POPL '01 Proceedings of the 28th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
POPL '77 Proceedings of the 4th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Partial Completeness of Abstract Fixpoint Checking
SARA '02 Proceedings of the 4th International Symposium on Abstraction, Reformulation, and Approximation
Construction of Abstract State Graphs with PVS
CAV '97 Proceedings of the 9th International Conference on Computer Aided Verification
LICS '04 Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science
Termination proofs for systems code
Proceedings of the 2006 ACM SIGPLAN conference on Programming language design and implementation
CAV '08 Proceedings of the 20th international conference on Computer Aided Verification
Proving Conditional Termination
CAV '08 Proceedings of the 20th international conference on Computer Aided Verification
COSTA: Design and Implementation of a Cost and Termination Analyzer for Java Bytecode
Formal Methods for Components and Objects
Size-Change Termination, Monotonicity Constraints and Ranking Functions
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
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ACM Transactions on Programming Languages and Systems (TOPLAS)
Multi-dimensional rankings, program termination, and complexity bounds of flowchart programs
SAS'10 Proceedings of the 17th international conference on Static analysis
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Termination analysis with compositional transition invariants
CAV'10 Proceedings of the 22nd international conference on Computer Aided Verification
Abstraction refinement for termination
SAS'05 Proceedings of the 12th international conference on Static Analysis
Deciding conditional termination
TACAS'12 Proceedings of the 18th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Termination proofs for linear simple loops
SAS'12 Proceedings of the 19th international conference on Static Analysis
On the linear ranking problem for integer linear-constraint loops
POPL '13 Proceedings of the 40th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Eventual linear ranking functions
Proceedings of the 15th Symposium on Principles and Practice of Declarative Programming
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We present a novel technique for proving program termination which introduces a new dimension of modularity. Existing techniques use the program to incrementally construct a termination proof. While the proof keeps changing, the program remains the same. Our technique goes a step further. We show how to use the current partial proof to partition the transition relation into those behaviors known to be terminating from the current proof, and those whose status (terminating or not) is not known yet. This partition enables a new and unexplored dimension of incremental reasoning on the program side. In addition, we show that our approach naturally applies to conditional termination which searches for a precondition ensuring termination. We further report on a prototype implementation that advances the state-of-the-art on the grounds of termination and conditional termination.