Computable Obstructions to Wait-free Computability

Abstract. We show how to associate e ectively computableobstructions to a waitfree distributed decision task (I;O; ) in the asynchronous shared-memory, readwrite model. The key new ingredient of this work is the association of a simplicial complex T , the task complex, to the input-output relation . There is a simplicial map fromthe taskcomplexto theinputcomplexI, and is determinedby thetask. The existenceof a wait-freeprotocolsolvingthe taskimpliesthatthe map induced in homology must surject, and thus the non-zero elements of the cokernel of are obstructionsto solvability of the task. These obstructions are e ectivelycomputable when using suitable homologytheories, such as mod-2 simplicialhomology. Functors other than homology can be substituted, although the obstructions obtained may not be computable. We also extend the Herlihy-Shavit Theorem on Spans to the case of protocols that are anonymous relative to the action of a group, provided the action is suitably rigid. For such rigid ...

• Type: Conference
• Year: 1997
• Where: FOCS
• Authors: John Havlicek
• Keywords: Decision Task, FOCS 1997, Simplicial Map Fromthe, Task Complex, Theoretical Computer Science