Learning Automata with Name Allocation
This provides incremental algorithmic tools for researchers in formal methods and data processing, enabling automated analysis of systems with infinite data domains.
The paper tackles the problem of learning automata over infinite alphabets, which model data structures like cryptographic nonces or XML values, by introducing active learning methods for bar automata that adapt existing finite-alphabet learners with query complexity preserved, achieving the first such methods for infinite words and trees.
Automata over infinite alphabets have emerged as a convenient computational model for processing structures involving data, such as nonces in cryptographic protocols or data values in XML documents. We introduce active learning methods for bar automata, a species of automata that process finite data words represented as bar strings, which are words with explicit name binding letters. Bar automata have pleasant algorithmic properties. We develop a framework in which every learning algorithm for standard deterministic or nondeterministic finite automata over finite alphabets can be used to learn bar automata, with a query complexity determined by that of the chosen learner. The technical key to our approach is the algorithmic handling of $α$-equivalence of bar strings, which allows bridging the gap between finite and infinite alphabets. The principles underlying our framework are generic and also apply to bar Büchi automata and bar tree automata, leading to the first active learning methods for data languages of infinite words and finite trees.