24,736 research outputs found
Learn with SAT to Minimize B\"uchi Automata
We describe a minimization procedure for nondeterministic B\"uchi automata
(NBA). For an automaton A another automaton A_min with the minimal number of
states is learned with the help of a SAT-solver.
This is done by successively computing automata A' that approximate A in the
sense that they accept a given finite set of positive examples and reject a
given finite set of negative examples. In the course of the procedure these
example sets are successively increased. Thus, our method can be seen as an
instance of a generic learning algorithm based on a "minimally adequate
teacher" in the sense of Angluin.
We use a SAT solver to find an NBA for given sets of positive and negative
examples. We use complementation via construction of deterministic parity
automata to check candidates computed in this manner for equivalence with A.
Failure of equivalence yields new positive or negative examples. Our method
proved successful on complete samplings of small automata and of quite some
examples of bigger automata.
We successfully ran the minimization on over ten thousand automata with
mostly up to ten states, including the complements of all possible automata
with two states and alphabet size three and discuss results and runtimes;
single examples had over 100 states.Comment: In Proceedings GandALF 2012, arXiv:1210.202
Learning probability distributions generated by finite-state machines
We review methods for inference of probability distributions generated by probabilistic automata and related models for sequence generation. We focus on methods that can be proved to learn in the inference
in the limit and PAC formal models. The methods we review are state merging and state splitting methods for probabilistic deterministic automata and the recently developed spectral method for nondeterministic probabilistic automata. In both cases, we derive them from a high-level algorithm described in terms of the Hankel matrix of the distribution to be learned, given as an oracle, and then describe how to adapt that algorithm to account for the error introduced by a finite sample.Peer ReviewedPostprint (author's final draft
E-Generalization Using Grammars
We extend the notion of anti-unification to cover equational theories and
present a method based on regular tree grammars to compute a finite
representation of E-generalization sets. We present a framework to combine
Inductive Logic Programming and E-generalization that includes an extension of
Plotkin's lgg theorem to the equational case. We demonstrate the potential
power of E-generalization by three example applications: computation of
suggestions for auxiliary lemmas in equational inductive proofs, computation of
construction laws for given term sequences, and learning of screen editor
command sequences.Comment: 49 pages, 16 figures, author address given in header is meanwhile
outdated, full version of an article in the "Artificial Intelligence
Journal", appeared as technical report in 2003. An open-source C
implementation and some examples are found at the Ancillary file
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