Automata Learning with Automated Alphabet Abstraction Refinement

Abstract

Abstraction is the key when learning behavioral models of realistic systems, but also the cause of a major problem: the introduction of non-determinism. In this paper, we introduce a method for refining a given abstraction to automatically regain a deterministic behavior onthe-fly during the learning process. Thus the control over abstraction becomes part of the learning process, with the effect that detected nondeterminism does not lead to failure, but to a dynamic alphabet abstraction refinement. Like automata learning itself, this method in general is neither sound nor complete, but it also enjoys similar convergence properties even for infinite systems as long as the concrete system itself behaves deterministically, as illustrated along a concrete example.

Learning of Automata Models Extended with Data

“…We concentrated on presenting an approach that adapts ideas using abstraction that have been successfully applied in formal verification. This approach has been used on some nontrivial examples [1,2], and techniques for revising abstractions by need have been developed [19]. However, it is clear that much work remains in order to make automata learning with data easily applicable to a wide class of systems.…”

“…This can be achieved by letting each possible guard correspond to a different abstract input symbol. For the case that the abstraction is not fine enough to distinguish between symbolic transitions that cause different output, a technique for refining the abstraction on-the-fly, during the learning process, has been developed by Howar, Steffen, and Merten [19]. -The abstraction should be unambiguous.…”

Learning Assumptions for CompositionalVerification of Timed Systems

“…Howar et al [22] also used the paradigm on the alphabet for inferring abstract λ (a, xa = 3) λ 1 0 (s0) (a, xa = 0) 0 0 (s1) (a, xa = 1) 1 1 (s2) (a, xa = 2) 0 0 (a, xa = 3) 0 0 (a, xa ≥ 3) 0 0 (a, 0 ≤ xa ≤ 1) 0 0 (a, 1 ≤ xa ≤ 2) 0 0 (a, 2 ≤ xa ≤ 3) 0 0 (a, 0 ≤ xa ≤ 2) 0 0 (a, 1 ≤ xa ≤ 3) 0 0 (a, 0 ≤ xa ≤ 3) 0 0 (a, xa = 0)(a, xa = 0) 0 0 (a, xa = 0)(a, xa = 1) 0 0 (a, xa = 0)(a, xa = 2) 0 0 (a, xa = 0)(a, xa = 3) 0 0 (a, xa = 0)(a, xa ≥ 3) 0 0 (a, xa = 0)(a, 0 ≤ xa ≤ 1) 0 0 (a, xa = 0)(a, 1 ≤ xa ≤ 2) 0 0 (a, xa = 0)(a, 2 ≤ xa ≤ 3) 0 0 (a, xa = 0)(a, 0 ≤ xa ≤ 2) 0 0 (a, xa = 0)(a, 1 ≤ xa ≤ 3) 0 0 (a, xa = 0)(a, 0 ≤ xa ≤ 3) 0 0 (a, xa = 1)(a, xa = 0) 0 0 (a, xa = 1)(a, xa = 1) 0 0 (a, xa = 1)(a, xa = 2) 0 0 (a, xa = 1)(a, xa = 3) 1 0 (a, xa = 1)(a, xa ≥ 3) 0 0 (a, xa = 1)(a, 0 ≤ xa ≤ 1) 0 0 (a, xa = 1)(a, 1 ≤ xa ≤ 2) 0 0 (a, xa = 1)(a, 2 ≤ xa ≤ 3) 0 0 (a, xa = 1)(a, 0 ≤ xa ≤ 2) 0 0 (a, xa = 1)(a, 1 ≤ xa ≤ 3) 0 0 (a, xa = 1)(a, 0 ≤ xa ≤ 3) 0 0 Table Constructed by TL * sg automata with respect to given concrete behavior such that determinism is preserved. Our TL * algorithm may benefit from the abstraction refinement paradigm if the alphabet of the ERA to be learned can be smaller.…”

Machine Learning for Emergent Middleware

“…The more structured the intended learning output is, the more successful active learning will be, as the required structural constraints are a good guide for the active construction of examples [3]. It has been successfully used in practice for inferring computational models via testing [10,9].…”