Theory of linear and integer programming
Theory of linear and integer programming
ACM Transactions on Programming Languages and Systems (TOPLAS)
International Journal of Parallel Programming
Higher-Order and Symbolic Computation
Scheduling and Automatic Parallelization
Scheduling and Automatic Parallelization
An Exact Method for Analysis of Value-based Array Data Dependences
Proceedings of the 6th International Workshop on Languages and Compilers for Parallel Computing
Transitive Closure of Infinite Graphs and Its Applications
LCPC '95 Proceedings of the 8th International Workshop on Languages and Compilers for Parallel Computing
On the Equivalence of Two Systems of Affine Recurrence Equations (Research Note)
Euro-Par '02 Proceedings of the 8th International Euro-Par Conference on Parallel Processing
Automatic Parallelization in the Polytope Model
The Data Parallel Programming Model: Foundations, HPF Realization, and Scientific Applications
Symbolic Verification with Periodic Sets
CAV '94 Proceedings of the 6th International Conference on Computer Aided Verification
Multiple Counters Automata, Safety Analysis and Presburger Arithmetic
CAV '98 Proceedings of the 10th International Conference on Computer Aided Verification
PACT '99 Proceedings of the 1999 International Conference on Parallel Architectures and Compilation Techniques
Code Generation in the Polyhedral Model Is Easier Than You Think
Proceedings of the 13th International Conference on Parallel Architectures and Compilation Techniques
Theoretical Computer Science - Implementation and application of automata
FAST: acceleration from theory to practice
International Journal on Software Tools for Technology Transfer (STTT)
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,
Computing the Transitive Closure of a Union of Affine Integer Tuple Relations
COCOA '09 Proceedings of the 3rd International Conference on Combinatorial Optimization and Applications
Equivalence Checking of Static Affine Programs Using Widening to Handle Recurrences
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
Coarse-Grained Loop Parallelization: Iteration Space Slicing vs Affine Transformations
ISPDC '09 Proceedings of the 2009 Eighth International Symposium on Parallel and Distributed Computing
Accelerated Invariant Generation for C Programs with Aspic and C2fsm
Electronic Notes in Theoretical Computer Science (ENTCS)
A Modular Static Analysis Approach to Affine Loop Invariants Detection
Electronic Notes in Theoretical Computer Science (ENTCS)
isl: an integer set library for the polyhedral model
ICMS'10 Proceedings of the Third international congress conference on Mathematical software
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part I
The power of hybrid acceleration
CAV'06 Proceedings of the 18th international conference on Computer Aided Verification
LEVER: a tool for learning based verification
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
Towards a model-checker for counter systems
ATVA'06 Proceedings of the 4th international conference on Automated Technology for Verification and Analysis
Equivalence checking of static affine programs using widening to handle recurrences
ACM Transactions on Programming Languages and Systems (TOPLAS)
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The set of paths in a graph is an important concept with many applications in system analysis. In the context of integer tuple relations, which can be used to represent possibly infinite graphs, this set corresponds to the transitive closure of the relation representing the graph. Relations described using only affine constraints and projection are fairly efficient to use in practice and capture Presburger arithmetic. Unfortunately, the transitive closure of such a quasi-affine relation may not be quasi-affine and so there is a need for approximations. In particular, most applications in system analysis require overapproximations. Previous work has mostly focused either on underapproximations or special cases of affine relations. We present a novel algorithm for computing overapproximations of transitive closures for the general case of quasi-affine relations (convex or not). Experiments on non-trivial relations from real-world applications show our algorithm to be on average more accurate and faster than the best known alternatives.