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## User: abhisek-midya

### Title: A Myhill-Nerode Theorem for Register Automata and Symbolic Trace Languages

We propose a new symbolic trace semantics for register automata (extended
finite state machines) which records both the sequence of input symbols that
occur during a run as well as the constraints on input parameters that are
imposed by this run. Our main result is a generalization of the classical
Myhill-Nerode theorem to this symbolic setting. Our generalization requires the
use of three relations to capture the additional structure of register
automata. Location equivalence $\equiv_l$ captures that symbolic traces end in
the same location, transition equivalence $\equiv_t$ captures that they share
the same final transition, and a partial equivalence relation $\equiv_r$
captures that symbolic values $v$ and $v'$ are stored in the same register
after symbolic traces $w$ and $w'$, respectively. A symbolic language is
defined to be regular if relations $\equiv_l$, $\equiv_t$ and $\equiv_r$ exist
that satisfy certain conditions, in particular, they all have finite index. We
show that the symbolic language associated to a register automaton is regular,
and we construct, for each regular symbolic language, a register automaton that
accepts this language. Our result provides a foundation for grey-box learning
algorithms in settings where the constraints on data parameters can be
extracted from code using e.g. tools for symbolic/concolic execution or
tainting. We believe that moving to a grey-box setting is essential to overcome
the scalability problems of state-of-the-art black-box learning algorithms.

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The first result in this paper provides a very general $\epsilon$-removal argument for the multilinear restriction estimate. The second result …