Polynomial Identification of $$\omega $$-Automata

We study identification in the limit using polynomial time and data for models of $$\omega $$-automata. On the negative side we show that non-deterministic $$\omega $$-automata (of types Büchi, coBüchi, Parity or Muller) can not be polynomially learned in the limit. On the positive side we show that the $$\omega $$-language classes $$\mathbb {IB}$$, $$\mathbb {IC}$$, $$\mathbb {IP}$$, and $$\mathbb {IM}$$ that are defined by deterministic Büchi, coBüchi, parity, and Muller acceptors that are isomorphic to their right-congruence automata (that is, the right congruences of languages in these classes are fully informative) are identifiable in the limit using polynomial time and data. We further show that for these classes a characteristic sample can be constructed in polynomial time.

A Survey of State Merging Strategies for DFA Identification in the Limit

Identication of deterministic nite automata (DFAs) has an extensive history, both in passive learning and in active learning. Intractability results by Gold [5] and Angluin [1] show that nding the smallest automaton consistent with a set of accepted and rejected strings is NP-complete. Nevertheless, a lot of work has been done on learning DFAs from examples within specic heuristics, starting with Trakhtenbrot and Barzdin's algorithm [15], rediscovered and applied to the discipline of grammatical inference by Gold [5]. Many other algorithms have been developed, the convergence of most of which is based on characteristic sets: RPNI (Regular Positive and Negative Inference) by J. Oncina and P. García [11, 12], Traxbar by K. Lang [8], EDSM (Evidence Driven State Merging), Windowed EDSM and Blue- Fringe EDSM by K. Lang, B. Pearlmutter and R. Price [9], SAGE (Self-Adaptive Greedy Estimate) by H. Juillé [7], etc. This paper provides a comprehensive study of the most important state merging strategies developed so far.