Communications of the ACM - Special issue on parallelism
Theory of recursive functions and effective computability
Theory of recursive functions and effective computability
Handbook of logic in computer science (vol. 1)
The undecidability of aliasing
ACM Transactions on Programming Languages and Systems (TOPLAS)
CCL: A Portable and Tunable Collective Communication Library for Scalable Parallel Computers
IEEE Transactions on Parallel and Distributed Systems
Limits to parallel computation: P-completeness theory
Limits to parallel computation: P-completeness theory
Undecidability of context-sensitive data-dependence analysis
ACM Transactions on Programming Languages and Systems (TOPLAS)
Context-sensitive synchronization-sensitive analysis is undecidable
ACM Transactions on Programming Languages and Systems (TOPLAS)
MPI: The Complete Reference
Introduction to Automata Theory, Languages and Computability
Introduction to Automata Theory, Languages and Computability
The complexity of loop programs
ACM '67 Proceedings of the 1967 22nd national conference
| Hi-index | 0.00 |
Associativity is required for the use of general scans and reductions in parallel languages. Some systems also require functions used with scans and reductions to be commutative. We prove the undecidability of both associativity and commutativity. Thus, it is impossible in general for a compiler to check for those conditions. We also prove the stronger result that the resulting relations fail to be recursively enumerable. We prove that these results hold for the kind of function subprograms of practical interest in such a situation: function subprograms that, due to syntactical restrictions, are guaranteed to halt. Thus, our results are stronger than one can obtain from Rice's Theorem. We also obtain limitations concerning the construction of functions and limitations concerning compiler-generated run-time checks. In addition, we prove an undecidability result about programmer-constructed run-time checks.