Ahstract-Complex event processing (CEP) over event streams has become increasingly important for real-time applications ranging from health care, supply chain management to busi ness intelligence. These monitoring applications submit complex queries to track sequences of events that match a given pattern.As these systems mature the need for increasingly complex nested sequence query support arises, while the state-of-art CEP systems mostly support the execution of flat sequence queries only. To assure real-time responsiveness and scalability for pattern detection even on huge volume high-speed streams, efficient processing techniques must be designed. In this paper, we first analyze the prevailing nested pattern query processing strategy and identify several serious shortcomings. Not only are substantial subsequences first constructed just to be subse quently discarded, but also opportunities for shared execution of nested subexpressions are overlooked. As foundation, we introduce NEEL, a CEP query language for expressing nested CEP pattern queries composed of sequence, negation, AND and OR operators. To overcome deficiencies, we design rewriting rules for pushing negation into inner subexpressions. Next, we devise a normalization procedure that employs these rules for flattening a nested complex event expression. To conserve CPU and memory consumption, we propose several strategies for efficient shared processing of groups of normalized NEEL subexpressions. These strategies include prefix caching, suffix clustering and customized "bit-marking" execution strategies. We design an optimizer to partition the set of all CEP sub expressions in a NEEL normal form into groups, each of which can then be mapped to one of our shared execution operators. Lastly, we evaluate our technologies by conducting a performance study to assess the CPU processing time using real-world stock trades data. Our results confirm that our NEEL execution in many cases performs 100 fold faster than the traditional iterative nested execution strategy for real stock market query workloads.

We present a new system of intersection types for a composition-free calculus of explicit substitutions with a rule for garbage collection, and show that it characterizes those terms which are strongly normalizing. This system extends previous work on the natural generalization of the classical intersection types system, which characterized head normalization and weak normalization, but was not complete for strong normalization. An important role is played by the notion of available variable in a term, which is a generalization of the classical notion of free variable.

We present a new system of intersection types for a composition-free calculus of explicit substitutions with a rule for garbage collection, and show that it characterizes those terms which are strongly normalizing. This system extends previous work on the natural generalization of the classical intersection types system, which characterized head normalization and weak normalization, but was not complete for strong normalization. An important role is played by the notion of available variable in a term, which is a generalization of the classical notion of free variable.

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We investigate some fundamental properties of the reduction relation in the untyped term calculus derived from Curien and Herbelin's λµ µ. The original λµ µ has a system of simple types, based on sequent calculus, embodying a Curry-Howard correspondence with classical logic; the significance of the untyped calculus of raw terms is that it is a Turing-complete language for computation with explicit representation of control as well as code. We define a type assignment system for the raw terms satisfying: a term is typable if and only if it is strongly normalizing. The intrinsic symmetry in the λµ µ calculus leads to an essential use of both intersection and union types; in contrast to other union-types systems in the literature, our system enjoys the Subject Reduction property.