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On Left-Monotone Deterministic Restarting Automata [chapter]

T. Jurdziński, F. Otto, F. Mráz, M. Plátek
2004 Lecture Notes in Computer Science  
The notion of left-monotonicity is introduced for the restarting automaton, and the expressive power of the various types of leftmonotone restarting automata is studied.  ...  We concentrate on the deterministic classes, as here the results differ greatly from those for the corresponding classes of (right-) monotone restarting automata.  ...  In Section 4 we will establish hierarchies with respect to the degree of left-monotonicity for the various types of deterministic restarting automata without auxiliary symbols, and in Section 5 we will  ... 
doi:10.1007/978-3-540-30550-7_21 fatcat:m2lyhxgjrvebpbqer3q4icehse

Sequential monotonicity for restarting automata

Tomasz Jurdziński, Friedrich Otto
2007 RAIRO - Theoretical Informatics and Applications  
However, for restarting automata with auxiliary symbols, all degrees of sequential monotonicity collapse to the first level, implying that RLWW-automata that are sequentially monotone of degree j for any  ...  For restarting automata without auxiliary symbols, this restricted variant still yields infinite hierarchies.  ...  It would give the first example of a strict hierarchy for restarting automata that use auxiliary symbols.  ... 
doi:10.1051/ita:2007013 fatcat:i6f2fwljdvcw3i3u5iyg5ls7hu

Restarting automata with restricted utilization of auxiliary symbols

Tomasz Jurdziński, Friedrich Otto
2006 Theoretical Computer Science  
Here we put restrictions on the way in which restarting automata use auxiliary symbols, and we investigate the influence of these restrictions on their expressive power.  ...  The most general models of restarting automata make use of auxiliary symbols in their rewrite operations, although this ability does not directly correspond to any aspect of the analysis by reduction.  ...  Acknowledgements The authors thank František Mráz and Martin Plátek from Charles University, Prague, for many very interesting and fruitful discussions on restarting automata in general and the topic of  ... 
doi:10.1016/j.tcs.2006.07.023 fatcat:xjvkvij6jfhznpzqa6v5kx2wce

Two-dimensional hierarchies of proper languages of lexicalized FRR-automata

Martin Plátek, Friedrich Otto, František Mráz
2009 Information and Computation  
within sentences, and the number of occurrences of auxiliary symbols (categories) in the sentences (words) of the corresponding characteristic language, which models the use of categories during the process  ...  Here we present the freely rewriting restarting automaton (FRR-automaton), which is a variant of the restarting automaton that is tuned towards modeling such phenomena.  ...  By requiring that the automata considered are lexicalized we restrict the lengths of the blocks of auxiliary symbols that are allowed on the tape by a constant.  ... 
doi:10.1016/j.ic.2009.02.011 fatcat:qyoxe2lcibfwxhxo6exznvqr3a

The degree of word-expansion of lexicalized RRWW-automata — A new measure for the degree of nondeterminism of (context-free) languages

F. Mráz, F. Otto, M. Plátek
2009 Theoretical Computer Science  
This measure is based on the number of occurrences of auxiliary symbols (categories) used for recognizing a language as the projection of its characteristic language onto its input alphabet.  ...  We study a measure for the degree of nondeterminism of (context-free) languages in terms of deterministic restarting automata that are (strongly) lexicalized.  ...  By requiring that the automata considered are lexicalized we restrict the lengths of the blocks of auxiliary symbols that are allowed on the tape by a constant.  ... 
doi:10.1016/j.tcs.2009.03.017 fatcat:e4wmz6ptkvefznvrqt52djqxie

Restarting automata with auxiliary symbols restricted by lookahead size

Natalie Schluter
2014 International Journal of Computer Mathematics  
We present a study on lookahead hierarchies for restarting automata with auxiliary symbols and small lookahead.  ...  In particular, we show that there are just two different classes of languages recognised RRWW automata, through the restriction of lookahead size.  ...  For all k ≥ 2 and X ∈ {left-mon, mon}, we have L(X-RRWW(k)) = CF L. Corollary 14. For all k ≥ 2, we have L(right-left-RRWW(k)) =LIN. The respective questions for RWW automata remain open.  ... 
doi:10.1080/00207160.2014.926005 fatcat:vxeexny6cfe2pgtmsem5zq36tm

On h-Lexicalized Restarting Automata

Martin Plátek, Friedrich Otto
2017 Electronic Proceedings in Theoretical Computer Science  
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  ...  original tool for the description of lexicalized syntax.  ...  The authors thank their colleague František Mráz for many helpful discussions on the results presented.  ... 
doi:10.4204/eptcs.252.21 fatcat:glmgxqea75cldhlsetgnqiakdi

Degrees of non-monotonicity for restarting automata

T. Jurdziński, F. Mráz, F. Otto, M. Plátek
2006 Theoretical Computer Science  
It is shown that for the various types of deterministic and nondeterministic (two-way) restarting automata without auxiliary symbols, these notions yield infinite hierarchies, and we compare these hierarchies  ...  In the literature various notions of monotonicity for restarting automata have been studied.  ...  of restarting automata with auxiliary symbols.  ... 
doi:10.1016/j.tcs.2006.08.029 fatcat:jresjmuxwbajvbzgs73ulnzylq

Learning Analysis by Reduction from Positive Data [chapter]

František Mráz, Friedrich Otto, Martin Plátek
2006 Lecture Notes in Computer Science  
Analysis by reduction is a linguistically motivated method for checking correctness of a sentence. It can be modelled by restarting automata.  ...  In this paper we propose a method for learning restarting automata which are strictly locally testable (SLT-R-automata).  ...  For a restarting automaton M = (Σ, Γ, I), the symbols from Γ − Σ are called auxiliary symbols.  ... 
doi:10.1007/11872436_11 fatcat:f2uoojy7xvdrfgrz2qieeg3b4m

Restarting Tree Automata [chapter]

Heiko Stamer, Friedrich Otto
2007 Lecture Notes in Computer Science  
Closure under linear tree homomorphisms/transductions Restricted variants of restarting tree automata with auxiliary symbols and decidable emptiness problem Yield and path languages of restarting tree  ...  W-suffix: The working alphabet G coincides with the input alphabet F, i.e., there are no auxiliary symbols available.  ... 
doi:10.1007/978-3-540-69507-3_44 fatcat:cexorrkjovclpivwsrrnde6qwe

Hierarchies of weakly monotone restarting automata

František Mráz, Friedrich Otto
2005 RAIRO - Theoretical Informatics and Applications  
automata without auxiliary symbols.  ...  We introduce a measure on the degree of weak monotonicity and show that the language classes obtained in this way form strict hierarchies for the various types of deterministic and nondeterministic restarting  ...  For the nondeterministic restarting automata it turned out that the use of auxiliary symbols is necessary to obtain a characterization of the class of context-free languages.  ... 
doi:10.1051/ita:2005021 fatcat:xg4zbwubpne6jf73lcnw5v74xq

On Parallel Communicating Grammar Systems and Correctness Preserving Restarting Automata [chapter]

Dana Pardubská, Martin Plátek, Friedrich Otto
2009 Lecture Notes in Computer Science  
This paper contributes to the study of Freely Rewriting Restarting Automata (FRR-automata) and Parallel Communicating Grammar Systems (PCGS), which both are useful models in computational linguistics.  ...  bounded by constants, can be transformed into a freely rewriting restarting automaton of a very restricted form.  ...  For each type X of restarting automata and each t ∈ N + , we use t -X to denote the class of X-automata that execute at most t rewrite steps in any cycle.  ... 
doi:10.1007/978-3-642-00982-2_56 fatcat:vf2bxpucg5cilhgsgoeqqwar4y

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

Friedrich Otto
2009 RAIRO - Theoretical Informatics and Applications  
In fact, many different models of restarting automata have been developed (see, e.g., [23] for an overview).  ...  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  ...  The author wants to thank Sylvain Schmitz from the Université de Nice at Sophia Antipolis for pointing him to the literature on LR-parsers and for very helpful comments on a preliminary version of this  ... 
doi:10.1051/ita/2009013 fatcat:pghe46jrpvbgzcwdcfxuuuzzsu

CD-Systems of Restarting Automata Governed by Explicit Enable and Disable Conditions [chapter]

Friedrich Otto
2010 Lecture Notes in Computer Science  
We show that, for each CD-system M of restarting automata and each mode m of operation considered by Messerschmidt and Otto, there exists a CD-system M of restarting automata of the same type as M that  ...  This is the first time that a non-monotone type of R-automaton without auxiliary symbols is shown to be as expressive as the corresponding type of RR-automaton.  ...  At least for strictly deterministic CD-systems of restarting automata without auxiliary symbols, that is, for strictly deterministic CD-RRand CD-RRW-systems, it does not hold as shown by the following  ... 
doi:10.1007/978-3-642-11266-9_52 fatcat:h7cd63ryuzhtbhrp3gxgiiacyi

Marcus t-contextual grammars and cut hierarchies and monotonicity for restarting automata

F. Mráz, F. Otto, M. Plátek, T. Jurdziński
2006 Theoretical Computer Science  
In the first part of the paper classes of languages are studied that are accepted by certain types of restarting automata with limited cut-index.  ...  If the selection mappings are regular and satisfy an additional locality restriction, then these grammars correspond in their expressive power to restarting automata with cut-index t.  ...  On the other hand, these types of restarting automata become strictly less expressive when we remove their ability to use auxiliary symbols [6, 26] .  ... 
doi:10.1016/j.tcs.2006.08.027 fatcat:glgmfwxnsbcn3ivcwt7pu57fju
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