Finite Automata for the Sub- and Superword Closure of CFLs: Descriptional and Computational Complexity

We answer two open questions by (Gruber, Holzer, Kutrib, 2009) on the state-complexity of representing sub- or superword closures of context-free grammars (CFGs): (1) We prove a (tight) upper bound of $2^{\mathcal{O}(n)}$ on the size of nondeterministic finite automata (NFAs) representing the subword closure of a CFG of size $n$. (2) We present a family of CFGs for which the minimal deterministic finite automata representing their subword closure matches the upper-bound of $2^{2^{\mathcal{O}(n)}}$ following from (1). Furthermore, we prove that the inequivalence problem for NFAs representing sub- or superword-closed languages is only NP-complete as opposed to PSPACE-complete for general NFAs. Finally, we extend our results into an approximation method to attack inequivalence problems for CFGs

Algebraic optimization of recursive queries

Over the past few years, much attention has been paid to deductive databases. They offer a logic-based interface, and allow formulation of complex recursive queries. However, they do not offer appropriate update facilities, and do not support existing applications. To overcome these problems an SQL-like interface is required besides a logic-based interface.\ud \ud In the PRISMA project we have developed a tightly-coupled distributed database, on a multiprocessor machine, with two user interfaces: SQL and PRISMAlog. Query optimization is localized in one component: the relational query optimizer. Therefore, we have defined an eXtended Relational Algebra that allows recursive query formulation and can also be used for expressing executable schedules, and we have developed algebraic optimization strategies for recursive queries. In this paper we describe an optimization strategy that rewrites regular (in the context of formal grammars) mutually recursive queries into standard Relational Algebra and transitive closure operations. We also describe how to push selections into the resulting transitive closure operations.\ud \ud The reason we focus on algebraic optimization is that, in our opinion, the new generation of advanced database systems will be built starting from existing state-of-the-art relational technology, instead of building a completely new class of systems

A Perfect Match for Reasoning, Explanation, and Reason Maintenance

Path query languages have been previously shown to com- plement RDF rule languages in a natural way and have been used as a means to implement the RDFS derivation rules. RPL is a novel path query language specifically designed to be incorporated with RDF rules and comes in three avors: Node-, edge- and path- avored expressions allow to express conditional regular expressions over the nodes, edges, or nodes and edges appearing on paths within RDF graphs. Providing reg- ular string expressions and negation, RPL is more expressive than other RDF path languages that have been proposed. We give a compositional semantics for RPL and show that it can be evaluated efficiently, while several possible extensions of it cannot

MSO definable string transductions and two-way finite state transducers

String transductions that are definable in monadic second-order (mso) logic (without the use of parameters) are exactly those realized by deterministic two-way finite state transducers. Nondeterministic mso definable string transductions (i.e., those definable with the use of parameters) correspond to compositions of two nondeterministic two-way finite state transducers that have the finite visit property. Both families of mso definable string transductions are characterized in terms of Hennie machines, i.e., two-way finite state transducers with the finite visit property that are allowed to rewrite their input tape.Comment: 63 pages, LaTeX2e. Extended abstract presented at 26-th ICALP, 199

An Analysis of Aspect Composition Problems

The composition of multiple software units does not always yield the desired results. In particular, aspect-oriented composition mechanisms introduce new kinds of composition problems. These are caused by different characteristics as compared to object-oriented composition, such as inverse dependencies. The aim of this paper is to contribute to the understanding of aspect-oriented composition problems, and eventually composition problems in a more general context. To this extent we propose and illustrate a systematic approach to analyze composition problems in a precise and concrete manner. In this approach we represent aspect-based composition mechanisms as transformation rules on program graphs. We explicitly model and show where composition problems occur, in a way that can easily be fully automated. In this paper we focus on structural superimposition (cf. intertype declarations) to illustrate our approach; this results in the identification of three categories of causes of composition problems. \u