Overall Objectives
Application Domains
New Software and Platforms
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## Section: New Results

### An Efficient Translation from a modal $\mu$-Calculus with Converse to Tree Automata

In [16], we presented a direct translation from a sub-logic of $\mu$-calculus to non-deterministic binary automata of finite trees. The logic is an alternation-free modal $\mu$-calculus, restricted to finite trees and where formulae are cycle-free. This logic is expressive enough to encode significant fragments of query languages (such as Regular XPath). The size of the generated automaton (the number of transitions) is bounded by ${2}^{n}$ where $n$ is the size of a Fischer-Ladner closure of the formula. This is an improvement over previous translations in ${2}^{{n}^{2}}$. We have implemented our translation. In practice, our prototype effectively decides static analysis problems that were beyond reach, such as the XPath containment problem with DTDs of significant size.