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A Rewriting-Based Approach to Trace Analysis

We present a rewriting-based algorithm for efficiently evaluating future time Linear Temporal Logic (LTL) formulae on finite execution traces online. While the standard models of LTL are infinite traces, finite traces appear naturally when testing and/or monitoring real applications that only run for limited time periods. The presented algorithm is implemented in the Maude executable specification language and essentially consists of a set of equations establishing an executable semantics of LTL using a simple formula transforming approach. The algorithm is further improved to build automata on-the-fly from formulae, using memoization. The result is a very efficient and small Maude program that can be used to monitor program executions. We furthermore present an alternative algorithm for synthesizing provably minimal observer finite state machines (or automata) from LTL formulae, which can be used to analyze execution traces without the need for a rewriting system, and can hence be used by observers written in conventional programming languages. The presented work is part of an ambitious runtime verification and monitoring project at NASA Ames, called PATHEXPLORER, and demonstrates that rewriting can be a tractable and attractive means for experimenting and implementing program monitoring logics.