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

F. Mráz, F. Otto, M. Plátek, T. Jurdziński
<span title="">2006</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/elaf5sq7lfdxfdejhkqbtz6qoq" style="color: black;">Theoretical Computer Science</a> </i> &nbsp;
These are RR-automata that are allowed to perform up to t deletion operations in each cycle that each delete a single factor only.  ...  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.  ...  t-RR-automata Up to now we have considered restarting automata that only execute a single rewrite operation per cycle.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.tcs.2006.08.027">doi:10.1016/j.tcs.2006.08.027</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/glgmfwxnsbcn3ivcwt7pu57fju">fatcat:glgmfwxnsbcn3ivcwt7pu57fju</a> </span>
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On h-Lexicalized Restarting Automata

Martin Plátek, Friedrich Otto
<span title="2017-08-21">2017</span> <i title="Open Publishing Association"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/qzezkwolyvf33pglm2jldjklca" style="color: black;">Electronic Proceedings in Theoretical Computer Science</a> </i> &nbsp;
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  ...  Following some previous studies on restarting automata, we introduce a refined model -the hlexicalized restarting automaton (h-RLWW).  ...  The authors thank their colleague František Mráz for many helpful discussions on the results presented.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4204/eptcs.252.21">doi:10.4204/eptcs.252.21</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/glmgxqea75cldhlsetgnqiakdi">fatcat:glmgxqea75cldhlsetgnqiakdi</a> </span>
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On the Gap-Complexity of Simple RL-Automata [chapter]

F. Mráz, F. Otto, M. Plátek
<span title="">2006</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
On the other hand, it is allowed to perform up to t rewrite (that is, delete) steps per cycle. Here we study the gap-complexity of these automata.  ...  This method is modelled by restarting automata.  ...  It is required that before the first restart step and also between any two restart steps, M executes at least one delete operation.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/11779148_9">doi:10.1007/11779148_9</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/7xo72bvyxrgvrgakdp46uucniq">fatcat:7xo72bvyxrgvrgakdp46uucniq</a> </span>
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Degrees of non-monotonicity for restarting automata

T. Jurdziński, F. Mráz, F. Otto, M. Plátek
<span title="">2006</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/elaf5sq7lfdxfdejhkqbtz6qoq" style="color: black;">Theoretical Computer Science</a> </i> &nbsp;
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.  ...  Beyond j -monotonicity In Corollary 8.7 we have seen that deterministic RL-automata are more powerful than the corresponding deterministic RR-automata.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.tcs.2006.08.029">doi:10.1016/j.tcs.2006.08.029</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/jresjmuxwbajvbzgs73ulnzylq">fatcat:jresjmuxwbajvbzgs73ulnzylq</a> </span>
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Correctness Preservation and Complexity of Simple RL-Automata [chapter]

H. Messerschmidt, F. Mráz, F. Otto, M. Plátek
<span title="">2006</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
We focus on the descriptional complexity of these automata, establishing two complexity measures that are both based on the description of t-sRL-automata in terms of socalled meta-instructions.  ...  On the other hand, it is allowed to perform up to t rewrite (that is, delete) steps per cycle.  ...  It is required that before the first restart step and also between any two restart steps, M executes at least one delete operation.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/11812128_16">doi:10.1007/11812128_16</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/mtfqpwtzmne2vnb67spup2euay">fatcat:mtfqpwtzmne2vnb67spup2euay</a> </span>
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Hierarchies of weakly monotone restarting automata

František Mráz, Friedrich Otto
<span title="">2005</span> <i title="EDP Sciences"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/foywj2stzfcwdln5izx2cxkroe" style="color: black;">RAIRO - Theoretical Informatics and Applications</a> </i> &nbsp;
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  ...  It is known that the weakly monotone restarting automata accept exactly the growing context-sensitive languages.  ...  In [3] it is shown that all variants of deterministic monotone restarting automata accept exactly the deterministic context-free languages.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1051/ita:2005021">doi:10.1051/ita:2005021</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/xg4zbwubpne6jf73lcnw5v74xq">fatcat:xg4zbwubpne6jf73lcnw5v74xq</a> </span>
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Left-to-right regular languages and two-way restarting automata

Friedrich Otto
<span title="2009-04-24">2009</span> <i title="EDP Sciences"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/foywj2stzfcwdln5izx2cxkroe" style="color: black;">RAIRO - Theoretical Informatics and Applications</a> </i> &nbsp;
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.  ...  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  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1051/ita/2009013">doi:10.1051/ita/2009013</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/pghe46jrpvbgzcwdcfxuuuzzsu">fatcat:pghe46jrpvbgzcwdcfxuuuzzsu</a> </span>
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Context-free languages can be accepted with absolutely no space overhead

Lane A. Hemaspaandra, Proshanto Mukherji, Till Tantau
<span title="">2005</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/joe2ngto45hbnl3pncnesnq344" style="color: black;">Information and Computation</a> </i> &nbsp;
no space overhead, and that all deterministic context-free languages can be accepted deterministically in polynomial time with absolutely no space overhead.  ...  The only work space the machines have, beyond the fixed amount of memory implicit in their finite-state control, is that which they can create by cannibalizing the input bits' own space.  ...  Many variants of restarting automata have been studied; see [22] for an overview.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.ic.2005.05.005">doi:10.1016/j.ic.2005.05.005</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/cncblpqlrbfotbeludfw5l2gwa">fatcat:cncblpqlrbfotbeludfw5l2gwa</a> </span>
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Two-dimensional hierarchies of proper languages of lexicalized FRR-automata

Martin Plátek, Friedrich Otto, František Mráz
<span title="">2009</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/joe2ngto45hbnl3pncnesnq344" style="color: black;">Information and Computation</a> </i> &nbsp;
We study proper languages of deterministic FRR-automata that are (strongly) lexicalized, where we focus on two types of constraints: the number of rewrites per cycle, which models the degree of valences  ...  Based on these constraints we obtain four variants of two-dimensional hierarchies of language classes.  ...  We have investigated the influence of two parameters on the expressive power of these automata: the number of rewrites per cycle, and the number of auxiliary symbols that may appear on the tape at the  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.ic.2009.02.011">doi:10.1016/j.ic.2009.02.011</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/qyoxe2lcibfwxhxo6exznvqr3a">fatcat:qyoxe2lcibfwxhxo6exznvqr3a</a> </span>
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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
<span title="">2009</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/elaf5sq7lfdxfdejhkqbtz6qoq" style="color: black;">Theoretical Computer Science</a> </i> &nbsp;
We study a measure for the degree of nondeterminism of (context-free) languages in terms of deterministic restarting automata that are (strongly) lexicalized.  ...  Our main results establish a hierarchy of classes of context-free languages and two hierarchies of classes of non-context-free languages that are based on the expansion factor of a language.  ...  Accordingly, we establish three hierarchies of language classes that are based on the word-expansion factor: one for monotone deterministic RRWW-automata that are (strongly) lexicalized, and two for the  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.tcs.2009.03.017">doi:10.1016/j.tcs.2009.03.017</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/e4wmz6ptkvefznvrqt52djqxie">fatcat:e4wmz6ptkvefznvrqt52djqxie</a> </span>
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Succinct description of regular languages by weak restarting automata

Martin Kutrib, Jens Reimann
<span title="">2008</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/joe2ngto45hbnl3pncnesnq344" style="color: black;">Information and Computation</a> </i> &nbsp;
We distinguish the classes of weak restarting automata, i.e., classical restarting automata accepting exactly the regular languages.  ...  The descriptional complexity of restarting automata is investigated.  ...  Therefore, we have to restrict the window size to one. In [14] it also has been shown that nondeterministic R(1)-automata accept exactly the regular languages.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.ic.2008.03.016">doi:10.1016/j.ic.2008.03.016</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/o3jrvwt4dzfpdaq5bxfk7kxwai">fatcat:o3jrvwt4dzfpdaq5bxfk7kxwai</a> </span>
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Overhead-Free Computation, DCFLs, and CFLs [article]

Lane A. Hemaspaandra, Proshanto Mukherji, Till Tantau
<span title="2004-10-15">2004</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
, and that all deterministic context-free languages can be accepted deterministically in polynomial time with absolutely no space overhead.  ...  The only work space the machines have, beyond the fixed amount of memory implicit in their finite-state control, is that which they can create by cannibalizing the input bits' own space.  ...  Many variants of restarting automata have been studied; see [Ott03] for an overview.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/cs/0410035v1">arXiv:cs/0410035v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/i6qtay3chfhffd4ffjpohv4k3q">fatcat:i6qtay3chfhffd4ffjpohv4k3q</a> </span>
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Page 573 of Mathematical Reviews Vol. , Issue 2003A [page]

<span title="">2003</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
He points out that the algorithm pre- sented in this paper is conceptually simpler and its time complexity depends only on the two input automata. Janusz J.  ...  In general, RRWW-automata can use auxiliary (working) symbols in rewriting. Subclasses of RRWW-automata have no working symbols and/or cannot rewrite but only delete symbols.  ... 
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On the Expressive Power of Stateless Ordered Restart-Delete Automata

Friedrich Otto
<span title="2021-03-13">2021</span> <i title="Springer Science and Business Media LLC"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/qj6jzeossfhihfshwf7nb7lbcq" style="color: black;">Theory of Computing Systems</a> </i> &nbsp;
These are obtained from the stateless ordered restarting automata (stl-ORWW-automata) by introducing an additional restart-delete operation, which, based on the surrounding context, deletes a single letter  ...  AbstractStateless ordered restart-delete automata (stl-ORD-automata) are studied.  ...  Acknowledgements The author thanks two anonymous reviewers for their very detailed comments on an Theory of Computing Systems material.  ... 
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On determinism versus nondeterminism for restarting automata

Hartmut Messerschmidt, Friedrich Otto
<span title="">2008</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/joe2ngto45hbnl3pncnesnq344" style="color: black;">Information and Computation</a> </i> &nbsp;
By counting the number of cycles it may take M to detect this error, we obtain a measure for the influence that errors have on computations.  ...  Our first result states that for each type of restarting automaton X ∈ {R,RW,RWW,RL,RLW,RLWW}, if M is a nondeterministic X-automaton that is correctness preserving, then there exists a deterministic X-automaton  ...  We use the prefix det-to denote deterministic classes of restarting automata. We observe that any finite computation of a two-way restarting automaton M consists of certain phases.  ... 
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