Expressiveness and Complexity of Crosscut Languages

Selector languages, or crosscut languages, play an important role in aspect-oriented programming (AOP). Examples of prominent selector languages include the pointcut language in AspectJ, traversal specifications in Demeter, XPath for databases, and regular expressions. A selector language expression, also referred to as a selector, selects nodes on an instance graph (an execution tree or an object tree) that satisfies a meta graph (a call graph or a class graph). The implementation of selector languages requires practically efficient algorithms for answering questions such as: does a selector always (never) select certain nodes Select-Always (Select-Never), does a selector ever select a node Select-Sat, does one selector imply another selector Select-Impl or does an edge in an instance graph lead to a node selected by the selector Select-Completion. We study these problems from the viewpoints of two important selector languages called SAJ, inspired by AspectJ, and SD, inspired by Demeter, and several of their sublanguages. We show a polynomial-time two-way reduction between SD and SAJ revealing interesting connections and promoting transfer of algorithmic techniques from AspectJ to Demeter and vice-versa. We characterize the complexity of these problems by either providing upper bounds, in the form of useful polynomial-time algorithms, or hardness results, showing them to be NP-complete or co-NP-complete. We present a fixed parameter tractable (FPT) algorithm for one of the NP-complete problems. This early result indicates a pragmatic line of attack for dealing with the intractability inherent in these problems. The algorithmic results contained herein should be of interest to developers of scalable AOP tools. We discuss the consequences of this paper for our DAJ implementation.