Termination detection in logic programs using argument sizes (extended abstract)
PODS '91 Proceedings of the tenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
How to Compose Presburger-Accelerations: Applications to Broadcast Protocols
FST TCS '02 Proceedings of the 22nd Conference Kanpur on Foundations of Software Technology and Theoretical Computer Science
LICS '04 Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science
Higher-Order and Symbolic Computation
Proceedings of the 35th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Proving Conditional Termination
CAV '08 Proceedings of the 20th international conference on Computer Aided Verification
TACAS '09 Proceedings of the 15th International Conference on Tools and Algorithms for the Construction and Analysis of Systems: Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2009,
Flat Parametric Counter Automata
Fundamenta Informaticae - Machines, Computations and Universality, Part II
Automata-Based Termination Proofs
CIAA '09 Proceedings of the 14th International Conference on Implementation and Application of Automata
Precise fixpoint computation through strategy iteration
ESOP'07 Proceedings of the 16th European conference on Programming
Verifying parametrised hardware designs via counter automata
HVC'07 Proceedings of the 3rd international Haifa verification conference on Hardware and software: verification and testing
An improved tight closure algorithm for integer octagonal constraints
VMCAI'08 Proceedings of the 9th international conference on Verification, model checking, and abstract interpretation
Termination of integer linear programs
CAV'06 Proceedings of the 18th international conference on Computer Aided Verification
Programs with lists are counter automata
CAV'06 Proceedings of the 18th international conference on Computer Aided Verification
Fast acceleration of ultimately periodic relations
CAV'10 Proceedings of the 22nd international conference on Computer Aided Verification
Linear ranking with reachability
CAV'05 Proceedings of the 17th international conference on Computer Aided Verification
Proving Termination by Policy Iteration
Electronic Notes in Theoretical Computer Science (ENTCS)
On the Termination of Integer Loops
ACM Transactions on Programming Languages and Systems (TOPLAS)
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
Counterexample-Guided precondition inference
ESOP'13 Proceedings of the 22nd European conference on Programming Languages and Systems
Eventual linear ranking functions
Proceedings of the 15th Symposium on Principles and Practice of Declarative Programming
Proving termination starting from the end
CAV'13 Proceedings of the 25th international conference on Computer Aided Verification
Hi-index | 0.00 |
This paper addresses the problem of conditional termination, which is that of defining the set of initial configurations from which a given program terminates. First we define the dual set, of initial configurations, from which a non-terminating execution exists, as the greatest fixpoint of the pre-image of the transition relation. This definition enables the representation of this set, whenever the closed form of the relation of the loop is definable in a logic that has quantifier elimination. This entails the decidability of the termination problem for such loops. Second, we present effective ways to compute the weakest precondition for non-termination for difference bounds and octagonal (non-deterministic) relations, by avoiding complex quantifier eliminations. We also investigate the existence of linear ranking functions for such loops. Finally, we study the class of linear affine relations and give a method of under-approximating the termination precondition for a non-trivial subclass of affine relations. We have performed preliminary experiments on transition systems modeling real-life systems, and have obtained encouraging results.