Optimizing Automata Learning via Monads

TL;DR

This paper introduces a monad-based framework for automata learning that improves scalability by enabling compact representations, supported by a new algorithm, correctness proofs, and a Haskell library implementation.

Contribution

It develops a parametric automata learning algorithm using monads, unifies existing methods, and provides a practical Haskell library with experimental validation.

Findings

New monad-based automata learning algorithm

Unified framework capturing existing and new algorithms

Experimental results on non-deterministic and weighted automata

Abstract

Automata learning has been successfully applied in the verification of hardware and software. The size of the automaton model learned is a bottleneck for scalability, and hence optimizations that enable learning of compact representations are important. This paper exploits monads, both as a mathematical structure and a programming construct, to design, prove correct, and implement a wide class of such optimizations. The former perspective on monads allows us to develop a new algorithm and accompanying correctness proofs, building upon a general framework for automata learning based on category theory. The new algorithm is parametric on a monad, which provides a rich algebraic structure to capture non-determinism and other side-effects. We show that our approach allows us to uniformly capture existing algorithms, develop new ones, and add optimizations. The latter perspective allows us to effortlessly translate the theory into practice: we provide a Haskell library implementing our general framework, and we show experimental results for two specific instances: non-deterministic and weighted automata.