Streaming Property Testing of Visibly Pushdown Languages *

Abstract : In the context of formal language recognition, we demonstrate the superiority of streaming property testers against streaming algorithms and property testers, when they are not combined. Initiated by Feigenbaum et al., a streaming property tester is a streaming algorithm recognizing a language under the property testing approximation: it must distinguish inputs of the language from those that are ε-far from it, while using the smallest possible memory (rather than limiting its number of input queries). Our main result is a streaming ε-property tester for visibly pushdown languages (Vpl) with memory space poly((log n)/ε). Our construction is done in three steps. First, we simulate a visibly pushdown automaton in one pass using a stack of small height but whose items can be of linear size. In a second step, those items are replaced by small sketches. Those sketches rely on a notion of suffix-sampling we introduce. This sampling is the key idea for taking benefit of both streaming algorithms and property testers in the third step. Indeed, the last step relies on a (non-streaming) property tester for weighted regular languages based on a previous tester by Alon et al. This tester can directly be used for streaming testing special cases of instances of Vpl that are already hard for both streaming algorithms and property testers. We then use it to decide the correctness of completed items, given their sketches, before removing them from the stack.
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Piotr Sankowski and Christos Zaroliagis. 24th Annual European Symposium on Algorithms (ESA 2016), Aug 2016, Aarhus, Denmark. Leibniz International Proceedings in Informatics (LIPIcs), 57, pp.17, Proceedings of the 24th Annual European Symposium on Algorithms (ESA 2016). 〈http://esa-symposium.org/index.php〉. 〈10.4230/LIPIcs.ESA.2016.43〉
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Nathanaël François, Frédéric Magniez, Michel De Rougemont, Olivier Serre. Streaming Property Testing of Visibly Pushdown Languages *. Piotr Sankowski and Christos Zaroliagis. 24th Annual European Symposium on Algorithms (ESA 2016), Aug 2016, Aarhus, Denmark. Leibniz International Proceedings in Informatics (LIPIcs), 57, pp.17, Proceedings of the 24th Annual European Symposium on Algorithms (ESA 2016). 〈http://esa-symposium.org/index.php〉. 〈10.4230/LIPIcs.ESA.2016.43〉. 〈hal-01362276〉

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