Polynomial-time computation via local inference relations

We consider the concept of a local set of inference rules. A local rule set can be automatically transformed into a rule set for which bottom-up evaluation terminates in polynomial time. The local-rule-set transformation gives polynomial-time evaluation strategies for a large variety of rule sets that cannot be given terminating evaluation strategies by any other known automatic technique. This article discusses three new results. First, it is shown that every polynomial-time predicate can be defined by an (unstratified) local rule set. Second, a new machine-recognizable subclass of the local rule sets is identified. Finally, we show that locality, as a property of rule sets, is undecidable in general.