Approximate schemas, source-consistency and query answering
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SOFSEM '10 Proceedings of the 36th Conference on Current Trends in Theory and Practice of Computer Science
Structural statistical software testing with active learning in a graph
ILP'07 Proceedings of the 17th international conference on Inductive logic programming
Using patterns in the behavior of the random surfer to detect webspam beneficiaries
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ICDT'07 Proceedings of the 11th international conference on Database Theory
Approximate planning and verification for large markov decision processes
Proceedings of the 27th Annual ACM Symposium on Applied Computing
Detecting Webspam Beneficiaries Using Information Collected by the Random Surfer
International Journal of Organizational and Collective Intelligence
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Inspired by Property Testing, we relax the classical satisfiability U |= F between a finite structure U of a class K and a formula F, to a notion of \varessilon-satisfiability U |=\varepsilon F, and the classical equivalence F_1 \equiv F_2 between two formulas F_1 and F_2, to \varepsilon-equivalence F1 \equiv_\varepsilon F2 for \varepsilon 0. We consider the class of strings and trees with the edit distance with moves, and show that these approximate notions can be efficiently decided. We use a statistical embedding of words (resp. trees) into l_1, which generalizes the original Parikh mapping, obtained by sampling O(f(\epsilon)) finite samples of the words (resp. trees). We give a tester for equality and membership in any regular language, in time independent of the size of the structure. Using our geometrical embedding, we can also test the equivalence between two regular properties on words, defined by Monadic Second Order formulas. Our equivalence tester has polynomial time complexity in the size of the automaton (or regular expression), for a fixed varepisolon, whereas the exact version of the equivalence problem is PSPACE-complete. Last, we extend the geometric embedding, and hence the tester algorithms, to infinite regular languages and to context-free languages. For context-free languages, the equivalence tester has an exponential time complexity, whereas the exact version is undecidable.% MathType!MTEF!2!1!+- % feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyyyIOlaaa!37B6! \[\equiv\]