#### DMCA

## Learning correction grammars

### Cached

### Download Links

- [www.researchgate.net]
- [www.researchgate.net]
- [www.comp.nus.edu.sg]
- DBLP

### Other Repositories/Bibliography

Venue: | Proceedings of the 20th Annual Conference on Learning Theory, 2007. To appear. 10 For u > 1, u; b 2 N, the |

Citations: | 1 - 0 self |

### Citations

350 |
Inductive inference of formal languages from positive data.
- Angluin
- 1980
(Show Context)
Citation Context ...notation for the immediate predecessor of a successor ordinal, then a notation for that successor ordinal is (by definition) 2 u . We omit the details of the definition of <o. Suppose ϕp(0), ϕp(1), ϕp=-=(2)-=-, . . . are each notations in <o order (see [39]). Suppose, then, that the corresponding ordinals are longer and longer initial segments of some limit ordinal which is their sup. For example, some suc... |

298 |
Toward a mathematical theory of inductive inference’,
- Blum, Blum
- 1975
(Show Context)
Citation Context ...< ∞}, otherwise. Let L = � i∈N Li. By definition Li �⊆ TxtBc ∗ (Mi): if Pi holds then, Mi does not have a TxtBc ∗ -locking sequence for Li, a necessary requirement for Mi to TxtBc ∗ -identify Li (see =-=[5, 25]-=- for details about locking sequences); if Pi does not hold, then Mi does not TxtBc ∗ -identify one of the finite subsets, content(σ), of Li — the σ which witnessed failure of Pi. We now show L ∈ Cor 2... |

170 |
A machine-independent theory of the complexity of recursive functions.
- Blum
- 1967
(Show Context)
Citation Context ...the program number i in the ϕ-system. We assume that multiple arguments are coded in some standard way [39] and suppress the explicit coding. By Φ we denote an arbitrary fixed Blum complexity measure =-=[6, 24]-=- for the ϕ-system. A partial recursive function Φ(·, ·) is said to be a Blum complexity measure for ϕ, if and only if the following two conditions are satisfied: (a) for all i and x, Φ(i, x)↓ if and o... |

164 |
Comparison of identification criteria for machine inductive inference
- Case, Smith
- 1983
(Show Context)
Citation Context ...E | L = ∗ N} witnesses (d). (e) can be proven by patching the input, along the same lines as InfEx ∗ ⊆ InfBc (see [12]). Harrington’s proof of R, the class all recursive functions, being in Bc ∗ (see =-=[14]-=-) can also be used to show (f). We omit the details. ⊓⊔ Essentially, the anomaly hierarchies {TxtI n }n∈N, with I ∈ {Ex, Bc} are very stable: 9 e.g., (b) and (c) show that the extra learning power of ... |

98 |
Machine inductive inference and language identification
- Case, Lynes
- 1982
(Show Context)
Citation Context ...t is M(T [n]) = e, for all but finitely many n. There are several criteria for a learning machine to be successful on a language. Below we define some of them. 11sDefinition 13 (Explanatory Learning, =-=[12, 23]-=-). Suppose a ∈ N ∪ {∗}. (a) M TxtEx a -identifies a text T just in case (∃i | Wi = a content(T )) (∀ ∞ n)[M(T [n]) = i]. (b) M TxtEx a -identifies an r.e. language L (written: L ∈ TxtEx a (M)) just in... |

45 | The power of vacillation in language learning
- Case
- 1999
(Show Context)
Citation Context ...stead of standard ones (i.e., the need of selfcorrections) may be compensated by an increase of learning power. In this respect we note that many of our results can be adapted to vacillatory learning =-=[10]-=-. TxtFex a b with b, a ∈ N ∪ {∗} is the vacillatory learning criterion allowing the learner to vacillate 24sbetween ≤ b a-variants of the target language, Cor u TxtFex a b is the version using correct... |

21 | Hierarchies of sets and degrees below 0
- Epstein, Haas, et al.
- 1979
(Show Context)
Citation Context ...ov Hierarchy is in terms of count-down functions from Onotations for constructive ordinals. Similar presentations, differing from but equivalent to the one originally given by Ershov, can be found in =-=[3, 16]-=-. Definition 2 (Count-Down Function). A computable function F : N × N → O is a countdown function if for all x and t, F (x, t + 1) ≤o F (x, t). For a binary function h(·, ·) we write h(x, ∞) for the l... |

19 |
Tradeos in inductive inference of nearly minimal sized programs
- Chen
- 1982
(Show Context)
Citation Context ...gramming system is employed). Also known is the adverse effect on learning power of requiring the final and correct grammars to be merely within a computable parsimony factor of minimal size grammars =-=[27, 15]-=- (but that the resulting inferring power is independent of the underlying acceptable programming system [20]). Hence, parsimony restrictions of even the weaker kind described just above limit inferrin... |

12 | Inductive Inference of automata, functions and programs - Bārzdiņˇs - 1974 |

12 | Inductive inference of automata, functions and programs - Bārzdiņš - 1974 |

12 |
Comparison of identi criteria for machine inductive inference
- Case, Smith
- 1983
(Show Context)
Citation Context ... 2 E j L = Ng witnesses (d). (e) can be proven by patching the input, along the same lines as InfEx InfBc (see [12]). Harrington's proof of R, the class all recursive functions, being in Bc (see =-=[14]-=-) can also be used to show (f). We omit the details. ut Essentially, the anomaly hierarchies fTxtIngn2N, with I 2 fEx;Bcg are very stable: 9 e.g., (b) and (c) show that the extra learning power of all... |

11 | Proof-theoretical analysis of termination proofs.
- Buchholz
- 1995
(Show Context)
Citation Context ...dely used in Proof Theory (e.g., to measure the strength of formal systems and classify their provably total functions) [42, 38], and in Term Rewriting (e.g., to prove termination of rewrite systems) =-=[7, 43]-=-. In Learning Theory, this idea has been introduced by Freivalds and Smith in [22]. They used ordinal notations, for example, for algorithmically counting down the mind-changes of inductive inference ... |

11 | On learning limiting programs
- Case, Jain, et al.
- 1992
(Show Context)
Citation Context ...ramatic increase of learning power compared to learning correction grammars of any ordinal complexity with less anomalies allowed. The proofs are straightforward lifts from other contexts (see, e.g., =-=[11]-=-). Theorem 36. For all u ∈ O, for all n ∈ N, (a) TxtEx 2n+1 − Cor u TxtBc n �= ∅. (b) TxtBc n+1 − Cor u TxtBc n �= ∅. (c) TxtEx n+1 − Cor u TxtEx n �= ∅. 22s(d) TxtEx ∗ − � n∈N Coru TxtBc n �= ∅. (e) ... |

6 |
Hierarchies of sets and degrees below 00
- Epstein, Haas, et al.
(Show Context)
Citation Context ...hov Hierarchy is in terms of count-down functions from Onotations for constructive ordinals. Similar presentations, diering from but equivalent to the one originally given by Ershov, can be found in =-=[3, 16]-=-. Denition 2 (Count-Down Function). A computable function F : NN ! O is a countdown function if for all x and t, F (x; t+ 1) o F (x; t). For a binary function h(; ) we write h(x;1) for the limit ... |

3 | Parsimony hierarchies for inductive inference
- Ambainis, Case, et al.
(Show Context)
Citation Context ...ion grammar. Equivalently, beginning with each item not included, we bound the number of mind-changes on the way to convergence of (total) procedures for limiting computable 0-1 valued functions (see =-=[1]-=- for another use of ordinal notations in the context of inductive inference of functions). We formalize the concept of a u-correction grammar, where u is a notation in O for some constructive ordinal.... |

3 |
Recursive structures and Ershov's hierarchy
- Ash, Knight
- 1996
(Show Context)
Citation Context ...tart with stage 1 for ease of notation). We will have the invariants that, at the start of stage s, (1) for x > xs + n, h(x, s) = 1 and F (x, s) = u. (2) for x < xs, for all t > s, h(x, t) = h(x, s). =-=(3)-=- For all xs ≤ x ≤ xs + n, either (3a) for i = M(h(·, s)[xs]), h(x, s) = 1 − θ u i (x, s), and F (x, s) = ψπ2(i)(x, s), or (3b) h(x, s) = 1, F (x, s) = u (in this case xs �= xs−1, where we take x0 = 0)... |

2 |
Grammars with prohibition and human-computer interaction
- Burgin
- 2005
(Show Context)
Citation Context ...nfinite ordinal ω. 1 Introduction and Motivation We investigate a new model in the context of Gold-style computability-theoretic learning theory (see [23, 25]): learning “correction grammars”. Burgin =-=[8]-=- suggested that knowing a language may feature a representation of the language in terms of two sets of rules, i.e., two grammars, say g1 and g2: g2 is used to “edit” errors of (make corrections to) g... |

1 |
Program size complexity of correction grammars
- Case, Royer
- 2006
(Show Context)
Citation Context ...nstructive transfinite. A correction grammar for an r.e. set will be a “description” of the r.e. set as belonging to some level of the Ershov Hierarchy. We will build on recent work by Case and Royer =-=[13]-=- who obtained succinctness results for correction grammars and developed useful, uniform numberings (i.e., programming systems) for the relevant classes of the Ershov Hierarchy. Using these programmin... |