Section: New Results

There is no complete linear term rewriting system for propositional logic

Participant : Lutz Straßburger.

Recently, we observed that the set of all sound linear inference rules in propositional logic is already coNP-complete  [84] . This means that every boolean tautology can be written as a (left-and right-) linear rewrite rule. This raises the question of whether there is a rewriting system on linear terms of propositional logic that is sound and complete for the set of all such rewrite rules. We have shown (in a joint work with Anupam Das) that, as long as reduction steps are polynomial-time decidable, such a rewriting system does not exist unless coNP=NP. This is published in [20] .