We consider the complexity of the emptiness problem for various classes of graph languages deened by eNCE (edge label neighborhood controlled embedding) graph grammars. In particular, we show that the emptiness problem is undecidable for general eNCE graph grammars, DEXPTIME-complete for connuent and boundary eNCE graph grammars, PSPACE-complete for linear eNCE graph grammars, NL-complete for d...

abstract: Recently, dependency pairs have greatly extended the provable class of terminating of term rewriting systems. The set of dependency pairs itself makes a term rewriting system. However, a term rewriting system and its dependency pairs do not accurately agree on the termination property. In this paper, we study the relation for the termination property between a term rewriting system, t...

A property P of term rewriting system is persistent if for any many-sorted term rewriting system R, R has the property P i its underlying term rewriting system (R), which results from R by omitting its sort information, has the property P. It is shown that termination is a persistent property of many-sorted term rewriting systems that contain only variables of the same sorts. This is the positi...

It is well known that the disjoint union of terminating term rewriting systems does not yield a terminating system in general. We show that this undesirable phenomenon vanishes if one implements term rewriting by graph reduction: given two terminating term rewrite systems 7~o and 7~1, the graph reduction system implementing 7~0 -F T~1 is terminating. In fact, we prove the stronger result that t...

A property is persistent if for any many-sorted term rewriting system , has the property if and only if term rewriting system , which results from by omitting its sort information, has the property . Zantema showed that termination is persistent for term rewriting systems without collapsing or duplicating rules. In this paper, we show that the Zantema’s result can be extended to term rewriting ...

We consider the problems of conjunctive query answering and rewriting under Description Logic constraints. We present a query rewriting algorithm for ELHI knowledge bases, and use it to show that query answering in this setting is PTime-complete w.r.t. data complexity. We show that our algorithm is worst-case optimal for languages with data complexity of query answering ranging from LogSpace to...

The direct sum of two term rewriting systems is the union of systems having disjoint sets of function symbols. It is shown that the direct sum of two term rewriting systems is not terminating, even if these systems are both terminating. Keyword: Term rewriting system, termination Introduction A term rewriting system R is a set of rewriting rules M → N , where M and N are terms [1, 3, 5]. The di...

Queries involving aggregation are typical in database applications. One of the main ideas to optimize the execution of an aggregate query is to reuse results of previously answered queries. This leads to the problem of rewriting aggregate queries using views. Due to a lack of theory, algorithms for this problem were rather ad-hoc. They were sound, but were not proven to be complete. Recently we...