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.