Recent years brought popularity and importance of complex event processing (CEP) and associated query languages. CEP systems can be hard to understand. It is often non-trivial to determine streams of events matched by a query, and sometimes we may not notice important edge cases. Hence, the desirability of formal semantics permitting reasoning about resulting complex events and checking if actual matchings agree with our intentions follows. In the article, we introduce a pattern language PatLang with some unique syntactic features related to variable binding. We provide two distinct denotational semantics for PatLang : Minimal semantics , sufficient to describe when patterns match, and tree semantics , which provides detailed information about subpatterns with which the matched events actually match, i.e., information about interpretation of matched events induced by the pattern matching. The tree semantics is unnecessary for verifying correctness of pattern matching execution. However, we show that neither minimal semantics, nor semantics from the prior work suffices to effectively locate errors in patterns with respect to their intended meaning, and that the additional information provided by the tree semantics is crucial for that purpose. We prove that tree semantics can be mapped to minimal semantics. Finally, we provide some practical evaluation.

Recent years brought increased popularity and importance of complex event processing (CEP) and associated query languages. CEP systems can easily become overwhelming and hard to understand. Hence the desirability of executable semantics and symbolic execution for CEP systems allowing for testing, simulation and verification. We demonstrate how constraint logic programming can be leveraged for the purpose by providing a proof-of-concept, non-deterministic semantics written in Prolog for a simple event stream matching language based on regular expressions. The semantics lends itself naturally to effective symbolic execution using narrowing combined with solving constraints. The result, aside from direct practical applications, is also of a more general interest as it demonstrates the benefits of combining narrowing (which provides constraint solving for general algebraic datatypes) with efficient constraint solvers for specific domains such as integer or real numbers.

We develop a multiset query and update language executable in a term rewriting system. Its most remarkable feature, besides non-standard approach to quantification and introduction of fresh values, is non-determinism - a query result is not uniquely determined by the database. We argue that this feature is very useful, e.g., in modelling user choices during simulation or reachability analysis of a data-centric business process - the intended application of our work. Query evaluation is implemented by converting the query into a terminating term rewriting system and normalizing the initial term which encapsulates the current database. A normal form encapsulates a query result. We prove that our language can express any relational algebra query. Finally, we present a simple business process specification framework (and an example specification). Both syntax and semantics of our query language is implemented in Maude. Comment: 40 pages, version edited by Fundamenta Informaticae

Recent years have seen the emergence of a data-centric approach to business process modelling as an attractive alternative to the dominant task-centric one. This new paradigm requires new tools for effective specification, simulation and validation of data-centric models. In particular, such tools must include support for expressive query and database update languages. Rewriting logic was proposed (and successfully used) as a generic framework for the specification of dynamic systems. However, though relational and other data models can be easily simulated, rewriting systems lack the direct support for first-order queries. In this paper we describe a novel condition and query language (at least as expressive as relational algebra), implemented in the term rewriting language Maude, together with a simple framework for relational transition system specification and simulation. The language is designed to be easy to implement on the top of a conditional rewriting system. Its most interesting feature is that it avoids all problems with variable binding. It works with models founded both on sets and multisets, and the language has linear-like facilities to refer to multiplicities of facts (in the case of multiset-founded models). As an example of the use of our language and simulation framework we reproduce some specifications of business processes from the literature. We also compare several methods for choosing the next action and its input during simulation.