We describe an automata-theoretic approach for the competitive analysis of online algorithms. Our approach is based on weighted automata, which assign to each input word a cost in IR ≥0 . By relating the "unbounded look ahead" of optimal offline algorithms with nondeterminism, and relating the "no look ahead" of online algorithms with determinism, we are able to solve problems about the competitive ratio of online algorithms, and the memory they require, by reducing them to questions about determinization and approximated determinization of weighted automata.

We describe an automata-theoretic approach for the competitive analysis of online algorithms. Our approach is based on weighted automata, which assign to each input word a cost in IR ≥0 . By relating the "unbounded look ahead" of optimal offline algorithms with nondeterminism, and relating the "no look ahead" of online algorithms with determinism, we are able to solve problems about the competitive ratio of online algorithms, and the memory they require, by reducing them to questions about determinization and approximated determinization of weighted automata.

System specifications are often structured as collections of scenarios and use-cases that describe desired and forbidden sequences of events. A recently proposed behavioral programming approach, which evolved from the visual language of live sequence charts (LSCs), calls for coding software modules in alignment with such scenarios. We present a methodology and a supporting model-checking tool for verifying behavioral Java programs, without having to first translate them into a specific input language for the model checker. Our method facilitates early discovery of conflicting or under-specified scenarios, which can often be resolved by adding new scenarios rather than by changing existing code. Also, counterexamples provided by the tool are themselves event sequences that can serve directly for refinements and corrections. Our tool reduces the size of the execution state-space using an abstraction that focuses on behaviorally interesting states and treats transitions between them as atomic.

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Abstract. In [AKL10], we showed how viewing online algorithms as reactive systems enables the application of ideas from formal verification to the competitive analysis of online algorithms. Our approach is based on weighted automata, which assign to each input word a cost in IR ≥0 . By relating the "unbounded look ahead" of optimal offline algorithms with nondeterminism, and relating the "no look ahead" of online algorithms with determinism, we were able to solve problems about the competitive ratio of online algorithms and the memory they require. In this paper we improve the application in three important and technically challenging aspects. First, we allow the competitive analysis to take into account assumptions about the environment. Second, we allow the online algorithm to have a bounded lookahead. Third, we describe a symbolic version of the model-checking algorithm and demonstrate its applicability. The first two contributions broaden the scope of our approach to settings in which the traditional analysis of online algorithms is particularly complicated. The third contribution improves the practicality of our approach and enables it to handle larger state spaces.