Testing Membership for Timed Automata

Given a timed automata which admits thick components and a timed word $x$, we present a tester which decides if $x$ is in the language of the automaton or if $x$ is $\epsilon$-far from the language, using finitely many samples taken from the weighted time distribution $\mu$ associated with an input $x$. We introduce a distance between timed words, the {\em timed edit distance}, which generalizes the classical edit distance. A timed word $x$ is $\epsilon$-far from a timed language if its relative distance to the language is greater than $\epsilon$.