Characteristic sets for polynomial grammatical inference

Inductive Synthesis of Cover-Grammars with the Help of Ant Colony Optimization

“…A similar concept has been studied in the context of automata [3]. Although any n-state deterministic finite automaton for some finite language L can be converted into a corresponding minimal cover-automaton, using only O(n log n) time [17], the construction of a minimal covergrammar seems to be intractable, specially in view of the following facts: (1) there is no polynomial-time algorithm for obtaining the smallest context-free grammar that generates exactly one given word (unless P = NP) [4]; (2) context-free grammar equivalence and even equivalence between a context-free grammar and a regular expression are undecidable [15]; (3) for any alphabet of a size of at least 2, the class of context-free grammars is not polynomially characterizable [12]; (4) the grammar can be exponentially smaller than any word in the language (an example is given in a book [14]). To our best knowledge there are no published algorithms for a cover-grammar problem defined as above.…”

Inductive Inference and Language Learning

“…The learning problem is then considered in the setting of identification in the limit from text with polynomial time and data introduced by de la Higuera [5]. For the sake of better readability we recall the definition here in the form used by Clark and Eyraud [4].…”

Teachability of a Subclass of Simple Deterministic Languages

“…In this problem, the learner finds out a correct hypothesis via a special set of examples. There are some different models of teachability [2], [4], [9]. In Goldman and Mathias's setting [2], the teacher makes a set of examples called teaching set which is helpful for the learner.…”

“…"Identification in the limit from polynomial time and data" is defined by de la Higuera [4]. This setting adds one more consistency condition to Goldman and Mathias's teachability, i.e.…”

“…It is shown by de la Higuera [4] that if a grammar class whose equivalence problem is undecidable then such class is not identifiable in the limit from polynomial time and data. It implies that such class of languages is not query learnable in polynomial time.…”