Restarting Automata and Their Relations to the Chomsky Hierarchy

Otto, Friedrich

doi:10.1007/3-540-45007-6_5

Cited by 38 publications

(16 citation statements)

References 26 publications

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“…From [9] we know that DCFL coincides with the class of languages that are accepted by monotone deterministic restarting automata without auxiliary symbols (that is, det-mon-RR-automata in the notation of [20]). Clearly each automaton of this form can be simulated by an FRR-automaton executing 408…”

Section: Constraints Of Word-ordermentioning

confidence: 99%

“…As defined in [9] (see also [20]), a restarting automaton is a nondeterministic machine that processes strings which are stored on a 'flexible' tape (or a list). It has a finite-state control, and it has a read/write window of a fixed size that works on this tape.…”

Section: Introductionmentioning

confidence: 99%

“…We emphasize the following nice properties of restarting automata, which are often used implicitly in proofs (see, e.g., [9,20,21]). …”

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confidence: 99%

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Free Word-Order and Restarting Automata

Mráz

Otto

Plátek

2014

Fundamenta Informaticae

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In natural languages with a high degree of word-order freedom, syntactic phenomena like dependencies (subordinations) or valences do not depend on the word-order (or on the individual positions of the individual words). This means that some permutations of sentences of these languages are in some (important) sense syntactically equivalent. Here we study this phenomenon in a formal way. Various types of j-monotonicity for restarting automata can serve as parameters for the degree of word-order freedom and for the complexity of word-order in sentences (languages). Here we combine two types of parameters on computations of restarting automata: the degree of j-monotonicity, and the number of rewrites per cycle. We study these notions formally in order to obtain an adequate tool for modelling and comparing formal descriptions of (natural) languages with different degrees of word-order freedom and word-order complexity.

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Section: Constraints Of Word-ordermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Free Word-Order and Restarting Automata

Mráz

Otto

Plátek

2014

Fundamenta Informaticae

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“…It consists in stepwise simplifications of a given extended sentence until a correct simple sentence is got or an error is found. To model ABR one can use the so-called restarting automata [5,10]. In this paper we propose a tool for design of restarting automata based on learning them from positive samples.…”

Section: Introductionmentioning

confidence: 99%

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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“…The restarting automaton [7,16,17], defining a set of simplification rules and a set of simple sentences, can be used to model the ABR. Such a model defines a language as a set of sentences, which can be simplified to a simple sentence of the model by the simplification rules of the model.…”

Section: Introductionmentioning

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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Restarting Automata and Their Relations to the Chomsky Hierarchy

Cited by 38 publications

References 26 publications

Free Word-Order and Restarting Automata

Free Word-Order and Restarting Automata

Learning Analysis by Reduction from Positive Data Using Reverible Languages

Power of S-kR-RRWW-automata

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