We introduce a fold operation that realises a tree-to-graph transduction by merging selected nodes in the input tree to form a possibly cyclic output graph. The work is motivated by the increasing use of graph-based representations in semantic parsing. We show that a suitable class of graphs languages can be generated by applying the fold operation to regular unranked tree languages. We investigate two versions of the fold operation, one that preserves a depth-first ordering between the edges, and one that does not. Finally, we demonstrate that the time complexity for the associated non-uniform membership problem is solvable in polynomial time for the order-preserving version, and NP-complete for the order-cancelling one.

It is well known that hyperedge-replacement grammars can generate NP-complete graph languages even under seemingly harsh restrictions. This means that the parsing problem is difficult even in the non-uniform setting, in which the grammar is considered to be fixed rather than being part of the input. Little is known about restrictions under which truly uniform polynomial parsing is possible. In this paper we propose a low-degree polynomial-time algorithm that solves the uniform parsing problem for a restricted type of hyperedge-replacement grammars which we expect to be of interest for practical applications.

Regular expressions are omnipresent in database applications. They form the structural core of schema languages for XML, they are a fundamental ingredient for navigational queries in graph databases, and are being considered in languages for upcoming technologies such as schema- and transformation languages for tabular data on the Web. In this paper we study the usage and effectiveness of the counting operator (or: limited repetition) in regular expressions. The counting operator is a popular extension which is part of the POSIX standard and therefore also present in regular expressions in grep, Java, Python, Perl, and Ruby. In a database context, expressions with counting appear in XML Schema and languages for querying graphs such as SPARQL 1.1 and Cypher.

Active context-free games are two-player games on strings over finite alphabets with one player trying to rewrite the input string to match a target specification. These games have been investigated in the context of exchanging Active XML (AXML) data. While it was known that the rewriting problem is undecidable in general, it is shown here that it is EXPSPACE-complete to decide for a given context-free game, whether all safely rewritable strings can be safely rewritten in a left-to-right manner, a problem that was previously considered by Abiteboul et al. Furthermore, it is shown that the corresponding problem for games with finite replacement languages is EXPTIME-complete.

Incremental view maintenance for XPath queries asks to maintain a materialized XPath view over an XML database. It assumes an underlying XML database D and a query Q . One is given a sequence of updates U to D , and the problem is to compute the result of Q ( U ( D )): the result of evaluating query Q on database D after having applied updates U . This article initiates a systematic study of the Boolean version of this problem. In the Boolean version, one only wants to know whether Q ( U ( D )) is empty or not. In order to quickly answer this question, we are allowed to maintain an auxiliary data structure. The complexity of the maintenance algorithms is measured in, (1) the size of the auxiliary data structure, (2) the worst-case time per update needed to compute Q ( U ( D )), and (3) the worst-case time per update needed to bring the auxiliary data structure up to date. We allow three kinds of updates: node insertion, node deletion, and node relabeling. Our main results are that downward XPath queries can be incrementally maintained in time O(depth( D )·poly(| Q |)) per update and conjunctive forward XPath queries in time O(depth( D ) · log(width( D ))·poly(| Q |)) per update, where | Q | is the size of the query, and depth( D ) and width( D ) are the nesting depth and maximum number of siblings in database D , respectively. The auxiliary data structures for maintenance are linear in | D | and polynomial in | Q | in all these cases.

We study the problem of incrementally maintaining an XPath query on an XML database under updates. The updates we consider are node insertion, node deletion, and node relabeling. Our main results are that downward XPath queries can be incrementally maintained in time O(depth(D) · poly(Q)) and conjunctive forward XPath queries in time O(depth(D)· log(width(D))·poly(Q)), where D is the size of the database, Q the size of the query, and depth(D) and width(D) are the nesting depth and maximum number of siblings in the database, respectively. The auxiliary data structures for maintenance are linear in D and polynomial in Q in all these cases.