On the representation of parallel search in theorem proving

This extended abstract summarizes two contributions from ongoing work on parallel search in theorem proving. First, we give a framework of definitions for parallel theorem proving, including inference system, communication operators, parallel search plan, subdivision function, parallel strategy, parallel derivation, fairness and propagation of redundancy for parallel derivations. A notion of a parallel strategy being a parallelization of a sequential strategy, and a theorem establishing a general relation between sequential fairness and parallel fairness are also given. Second, we extend our approach to the modelling of search to parallel search, covering inferences (expansion and contraction), behaviour of the search plan, subdivision of the search space and communication among the processes. This model allows us to study the behavior of many search processes on a single {\em marked search graph}. In the full paper, we plan to extend our methodology for the measure of the complexity of search in infinite spaces to parallel search, and apply it to obtain results in the comparison of strategies.