Learning Analysis by Reduction from Positive Data

Mráz, František; Otto, Friedrich; Plátek, Martin

doi:10.1007/11872436_11

Cited by 7 publications

(9 citation statements)

References 11 publications

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“…In this case, the reduction will be (λ, ab → λ, ab). In contrast, [9] assumes a helpful teacher that marks the subwords being rewritten.…”

Section: The Omega2 Methodsmentioning

confidence: 93%

“…Similarly, all the single sentences are accepted by the same accepting meta-instruction. In contrast [9] assumes a very helpful teacher that assigns the input samples to particular meta-instructions to be learned.…”

Section: The Omega2 Methodsmentioning

confidence: 97%

“…However, the achieved results are far from being applicable. A method of learning restarting automata from positive samples only was proposed in [9]. However, tests on neither artificial languages nor real ones were presented.…”

Section: Introductionmentioning

confidence: 98%

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Learning Analysis by Reduction from Positive Data Using Reverible Languages

Hoffmann

2008

2008 Seventh International Conference on Machine Learning and Applications

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The analysis by reduction [6,7,11] is a method for checking correctness of a sentence from a natural language. To model the analysis by reduction socalled restarting automata can be used. We propose a method for learning a special kind of restarting automata called single zero-reversible restarting automata (S-ZR-RRWW-automata). Interesting learning results achieved by using our implementation of the method are given. In addition the power of the model is investigated.

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“…In this case, the reduction will be (λ, ab → λ, ab). In contrast, [9] assumes a helpful teacher that marks the subwords being rewritten.…”

Section: The Omega2 Methodsmentioning

confidence: 93%

Section: The Omega2 Methodsmentioning

confidence: 97%

See 1 more Smart Citation

Learning Analysis by Reduction from Positive Data Using Reverible Languages

Hoffmann

2008

2008 Seventh International Conference on Machine Learning and Applications

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“…The method Omega * is similar to the approach of [14]. The considered model utilizes the kreversible languages [2, 13] instead of strictly locally testable languages.…”

Section: Definition 24 ([14])mentioning

confidence: 99%

“…A restarting automaton M is strictly k-testable (k-SLT-R-automaton), if all its metainstructions are strictly k-testable. A restarting automaton is strictly locally testable (SLT-R-automaton), if it is strictly k-testable for some k.The method Omega * is similar to the approach of [14]. The considered model utilizes the kreversible languages [2, 13] instead of strictly locally testable languages.…”

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confidence: 99%

Power of S-kR-RRWW-automata

Hoffmann

2015

Fundamenta Informaticae

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Single k-reversible restarting automata are a special version of restarting automata which can be effectively learned from samples. We show that their power lies between GCSL and CSL. We show that their subclasses form an infinite hierarchy of classes of languages with respect to the reversibility level k and we also show that limiting types of allowed rewrites lowers the power of the model. Finally, we study their relation to strictly locally testable restarting automata.One of the fundamental properties of all models of restarting automata is called the error preserving property. This property means that whenever a restarting automaton reduces a word from outside of the language accepted by that automaton ("the word contains an error"), the resulting word is not accepted by the automaton ("it contains still some error"), either. Proposition 2.2. (Error Preserving Property; [8])Let M = (Σ, Γ, I) be an RRWW-automaton, and let u, v be words over its input alphabet Σ. If u ⊢ * M v holds and u ∈ L(M ), then v ∈ L(M ), either.This proposition is extensively used for proving that some language cannot be accepted by any restarting automaton of a certain type (see [17]).The general RRWW-automata are not suitable for learning from positive samples only. Therefore in [14] a subclass of restarting automata, called strictly locally testable automata, was introduced, that is based on strictly locally testable languages [20,9]. Definition 2.3. ([20, 9])Let k > 0 and let Σ be an alphabet. A language L ⊆ Σ * is strictly k-testable if there exist finite sets A, B, C ⊆ Σ k such that for each w ∈ Σ ≥k , it holds that w ∈ L if and only if P k (w) ∈ A, S k (w) ∈ B, and I k (w) ⊆ C, where P k (w), S k (w), and I k (w) denote the k-length prefix of w, the k-length suffix of w, and the set of all interior subwords of length k of w. The tuple (A, B, C) is called a triple for L. A language L is called strictly locally testable if L is strictly k-testable for some k.The considered restriction proposed in the following definition allows the resulting model to learn from positive samples. Definition 2.4. ([14])Let k > 0. A rewriting meta-instruction (E ℓ , x → y, E r ) is strictly k-testable, if both E ℓ and E r are strictly k-testable and |x| ≤ k. An accepting meta-instruction (E, Accept) is strictly k-testable if E is strictly k-testable. A restarting automaton M is strictly k-testable (k-SLT-R-automaton), if all its metainstructions are strictly k-testable. A restarting automaton is strictly locally testable (SLT-R-automaton), if it is strictly k-testable for some k.The method Omega * is similar to the approach of [14]. The considered model utilizes the kreversible languages [2, 13] instead of strictly locally testable languages. Definition 2.5. ([2, 13])The FSA A is deterministic with lookahead k if for any pair p, q ∈ Q such that p = q, if p, q ∈ I or p, q ∈ δ(r, a) for some r ∈ Q, a ∈ Σ, then no word is a k-follower of both p and q.Moreover, the learning method Omega * has the following feature: for all u ∈ Γ + , v ∈ Γ * (Γ being the ...

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Compiler Generator Based on Restarting Automata

Procházka

2009

Implementation and Application of Automata

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Learning Analysis by Reduction from Positive Data

Cited by 7 publications

References 11 publications

Learning Analysis by Reduction from Positive Data Using Reverible Languages

Learning Analysis by Reduction from Positive Data Using Reverible Languages

Power of S-kR-RRWW-automata

Compiler Generator Based on Restarting Automata

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