Monotone Deterministic RL-Automata Don’t Need Auxiliary Symbols

Jurdziński, Tomasz; Mráz, František; Otto, Friedrich; Plátek, Martin

doi:10.1007/11505877_25

Cited by 6 publications

(5 citation statements)

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“…In [11] it is shown that monotone deterministic two-way restarting automata (that is, det-mon-RL-automata) define a language class that strictly includes the class DCFL, and that is rather robust in that it is also characterized by various other types of monotone deterministic two-way restarting automata. Actually, this class of languages is a proper subclass of CRL [23].…”

Section: Mathematics Subject Classification 68q45mentioning

confidence: 99%

“…Below we will need the details of a deterministic transducer that maps the language accepted by a left-monotone deterministic RL-automaton onto the reversal of a deterministic context-free language. Therefore, we provide a detailed description of this construction, which is actually simpler than a similar construction given in [11].…”

Section: Two-way Restarting Automatamentioning

confidence: 99%

“…In Section 2 we describe the types of restarting automata we will be dealing with in short. In addition, we provide a new, simplified proof for a result from [11] stating that a language that is accepted by a left-monotone deterministic RL-automaton can be transformed by an injective deterministic transduction into the reversal of a deterministic contextfree language. In Section 3 we restate the definition of the left-to-right regular grammars and languages and some of their main properties from [4].…”

Section: Introductionmentioning

confidence: 99%

“…The class CRL properly includes the deterministic context-free languages, but it is incomparable under inclusion to the class of unambiguous context-free languages [9]. The intersection of the classes CRL and CFL has been investigated only recently [13], and it has been shown that the problem of deciding whether a given Church-Rosser or context-free language belongs to this intersection is complete for the second level of the arithmetic hierarchy.In [11] it is shown that monotone deterministic two-way restarting automata (that is, det-mon-RL-automata) define a language class that strictly includes the class DCFL, and that is rather robust in that it is also characterized by various other types of monotone deterministic two-way restarting automata. Actually, this class of languages is a proper subclass of CRL [23].Here we show that the class of languages accepted by det-mon-RL-automata coincides with the class LRR of left-to-right regular languages.…”

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confidence: 99%

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Left-to-right regular languages and two-way restarting automata

Otto

2009

RAIRO-Theor. Inf. Appl.

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It is shown that the class of left-to-right regular languages coincides with the class of languages that are accepted by monotone deterministic RL-automata, in this way establishing a close correspondence between a classical parsing algorithm and a certain restricted type of analysis by reduction. Mathematics Subject Classification. 68Q45.Article published by EDP Sciences c EDP Sciences 2009 654 F. OTTO only a quadratic time bound in the worst case, even though this "rarely (if ever) occurs in practical situations" (see [2]). Further, these implementations can only handle certain subclasses of the left-to-right regular languages. The restarting automaton, on the other hand, was defined by Jančar et al.[7] to model the analysis by reduction, a technique used in linguistics to analyze sentences of natural languages with free word-order. A restarting automaton has a finitestate control and a read/write window of a fixed size that works on a flexible tape delimited by sentinels. It works in cycles. In each cycle it starts in its initial state with its read/write window in the leftmost position, scanning the left sentinel and the prefix of the current tape content. It can move its window on the tape one cell at a time by performing move-right and move-left steps until, at some place, it decides to rewrite the part of the tape content in its window by a shorter string, in this way also shortening the tape. After that it may perform further move operations until it eventually executes a restart. Such a restart places the window back over the left hand of the tape and resets the finite-state control to the initial state. Then the next cycle starts on the now shortened tape. The automaton halts by either performing an explicit accept instruction, or by entering a configuration for which its control unit has no further instructions, in which case it rejects.In fact, many different models of restarting automata have been developed (see, e.g., [23] for an overview). For example, monotone deterministic R-automata accept exactly the deterministic context-free languages, while monotone RLWWautomata characterize the class CFL of context-free languages [8]. Further, deterministic RWW-automata accept the Church-Rosser languages (CRL) of [15,19], which are of interest as they have linear-time decidable membership problems. Observe, however, that in general a deterministic restarting automaton (of any form) may execute up to n cycles on an input of length n, which yields a quadratic timebound. The class CRL properly includes the deterministic context-free languages, but it is incomparable under inclusion to the class of unambiguous context-free languages [9]. The intersection of the classes CRL and CFL has been investigated only recently [13], and it has been shown that the problem of deciding whether a given Church-Rosser or context-free language belongs to this intersection is complete for the second level of the arithmetic hierarchy.In [11] it is shown that monotone deterministic two-way restarting automata (that is, det-mon-RL-a...

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Section: Mathematics Subject Classification 68q45mentioning

confidence: 99%

Section: Two-way Restarting Automatamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Left-to-right regular languages and two-way restarting automata

Otto

2009

RAIRO-Theor. Inf. Appl.

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“…10,12,20,21] (a) CFL = L (mon-RWW) = L (mon-RRWW) = L (mon-RLWW). (b) LRR = L (det-mon-RL) = L (det-mon-RLW) = L (det-mon-RLWW).…”

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confidence: 99%

On h-Lexicalized Restarting Automata

Plátek

Otto

2017

Electron. Proc. Theor. Comput. Sci.

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Following some previous studies on restarting automata, we introduce a refined model -the hlexicalized restarting automaton (h-RLWW). We argue that this model is useful for expressing lexicalized syntax in computational linguistics. We compare the input languages, which are the languages traditionally considered in automata theory, to the so-called basic and h-proper languages, which are (implicitly) used by categorial grammars, the original tool for the description of lexicalized syntax. The basic and h-proper languages allow us to stress several nice properties of h-lexicalized restarting automata, and they are suitable for modeling the analysis by reduction and, subsequently, for the development of categories of a lexicalized syntax. Based on the fact that a two-way deterministic monotone restarting automaton can be transformed into an equivalent deterministic monotone RL-automaton in (Marcus) contextual form, we obtain a transformation from monotone RLWWautomata that recognize the class CFL of context-free languages as their input languages to deterministic monotone h-RLWW-automata that recognize CFL through their h-proper languages. Through this transformation we obtain automata with the complete correctness preserving property and an infinite hierarchy within CFL, based on the size of the read/write window. Additionally, we consider h-RLWW-automata that are allowed to perform multiple rewrite steps per cycle, and we establish another infinite hierarchy above CFL that is based on the number of rewrite steps that may be executed within a cycle. The corresponding separation results and their proofs illustrate the transparency of h-RLWW-automata that work with the (complete or cyclic) correctness preserving property.

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On Nonforgetting Restarting Automata That Are Deterministic and/or Monotone

Messerschmidt

Otto

2006

Computer Science – Theory and Applications

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Monotone Deterministic RL-Automata Don’t Need Auxiliary Symbols

Cited by 6 publications

References 6 publications

Left-to-right regular languages and two-way restarting automata

Left-to-right regular languages and two-way restarting automata

On h-Lexicalized Restarting Automata

On Nonforgetting Restarting Automata That Are Deterministic and/or Monotone

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