## Stratified context unification is npcomplete (2006)

Venue: | In Proc. of the 3rd International Joint Conference on Automated Reasoning, IJCAR’06 |

Citations: | 7 - 2 self |

### BibTeX

@INPROCEEDINGS{Levy06stratifiedcontext,

author = {Jordi Levy and Manfred Schmidt-schauß and Mateu Villaret},

title = {Stratified context unification is npcomplete},

booktitle = {In Proc. of the 3rd International Joint Conference on Automated Reasoning, IJCAR’06},

year = {2006},

pages = {82--96},

publisher = {SpringerVerlag}

}

### OpenURL

### Abstract

Abstract. Context Unification is the problem to decide for a given set of second-order equations E where all second-order variables are unary, whether there exists a unifier, such that for every second-order variable X, theabstractionλx.r instantiated for X has exactly one occurrence of the bound variable x in r. Stratified Context Unification is a specialization where the nesting of second-order variables in E is restricted. It is already known that Stratified Context Unification is decidable, NP-hard, and in PSPACE, whereas the decidability and the complexity of Context Unification is unknown. We prove that Stratified Context Unification is in NP by proving that a size-minimal solution can be represented in a singleton tree grammar of polynomial size, and then applying a generalization of Plandowski’s polynomial algorithm that compares compacted terms in polynomial time. This also demonstrates the high potential of singleton tree grammars for optimizing programs maintaining large terms. A corollary of our result is that solvability of rewrite constraints is NP-complete. 1