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On a subclass of context-free groups

Thomas Herbst
<span title="">1991</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;
Proposition 6.4 could be extended to all kinds of groups if it is possible to show that a group which is syntactic monoid of a deterministic contextfree language, is always a context-free group.  ...  DÉFINITION 2.7: A monoid M is called deterministic if every context-free language whose syntactic monoid is isomorphic to M is deterministic contextfree, and there is at least one of those.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1051/ita/1991250302551">doi:10.1051/ita/1991250302551</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/4o4fmessbnc2fn4cyuplwudb2u">fatcat:4o4fmessbnc2fn4cyuplwudb2u</a> </span>
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Page 3874 of Mathematical Reviews Vol. , Issue 98F [page]

<span title="">1998</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;
A basis of open sets of the Hall topology on the free monoid A* consists precisely of the group languages, so that a language is open if and only if it is a union (finite or infinite) of group languages  ...  Rational relations are rational subsets of a direct product of free monoids. Let M be a monoid and X C M.  ... 
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Page 3223 of Mathematical Reviews Vol. , Issue 86g [page]

<span title="">1986</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;
Author summary: “Given a context-free grammar G, the Hotz monoid [group] of G is the quotient of the free monoid [group] on the alphabet by the relations defined by the productions.  ...  If the grammar is right and left very-simple, this construction is simpler: the Hotz monoid is embeddable in the Hotz group, which is free, and the syntactical monoid is a Rees quotient of the Hotz monoid  ... 
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Context-free grammars with cancellation properties

Christiane Frougny
<span title="">1985</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;
Given a context-free grammar G the Hotz monoid (group) of G is the quotient of the free monoid (group) on the alphabet by the relations defined by the productions.  ...  In this case the Hotz monoid is embeddable in the Hotz group, which is free, and the syntactic monoid is a Rees quotient of the Hotz monoid.  ...  Now, since G is bi-very-simple, the letter x¢ never occurs in one of the rules P2,..., p, if we are in the first case for p~. So it is for xe if we are in the second case for p~.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0304-3975(85)90127-6">doi:10.1016/0304-3975(85)90127-6</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/orypjo6ubvcojjzazd7poddinq">fatcat:orypjo6ubvcojjzazd7poddinq</a> </span>
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Page 346 of Mathematical Reviews Vol. , Issue 80A [page]

<span title="">1980</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;
LR-deterministic grammars allow one to process com- plex contexts during the analysis phase and they are oriented to efficient bottom-up syntactic analysis.  ...  Two specific examples of outer measures on free monoids are discussed in connection with the linguistic facts.  ... 
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Page 6631 of Mathematical Reviews Vol. , Issue 88m [page]

<span title="">1988</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;
This does not hold true for +-languages for which it is well known that there exist finitely generated monoids which are not isomorphic to the syntactic monoid of a +-language. Klaus W.  ...  Eckehart Hotzel (D-GMD) 88m:68043 68Q70 03D05 20M35 68Q45 Jiirgensen, Helmut (3-WON-C); Thierrin, Gabriel (3-WON) Which monoids are syntactic monoids of w-languages?  ... 
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The loop problem for monoids and semigroups [article]

Mark Kambites
<span title="2006-09-11">2006</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We study also the case in which the loop problem is context-free, showing that a celebrated group-theoretic result of Muller and Schupp extends to describe completely simple semigroups with context-free  ...  We propose a way of associating to each finitely generated monoid or semigroup a formal language, called its loop problem.  ...  Acknowledgements This research was started while the author was at Carleton University supported by the Leverhulme Trust, and completed at Universität Kassel with the support of a Marie Curie Intra-European  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/math/0609293v1">arXiv:math/0609293v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/meh4sb7k3bczhnl4dkhakcpc5e">fatcat:meh4sb7k3bczhnl4dkhakcpc5e</a> </span>
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Syntactic Semigroups [chapter]

Jean-Eric Pin
<span title="">1997</span> <i title="Springer Berlin Heidelberg"> Handbook of Formal Languages </i> &nbsp;
Acknowledgements I would like to thank Jorge Almeida, Mario Branco and Pascal Weil for many useful suggestions on a rst version of this chapter.  ...  As was explained in the introduction, there are two parallel notions of languages. If we are working with monoids, a language on A is a subset of the free monoid A .  ...  Transductions were intensively studied in connection with context-free languages 19].  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-59136-5_10">doi:10.1007/978-3-642-59136-5_10</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/yvcpa66flrc6pgfpw5l27yma5q">fatcat:yvcpa66flrc6pgfpw5l27yma5q</a> </span>
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Page 2134 of Mathematical Reviews Vol. , Issue 85e [page]

<span title="">1985</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;
Author’s summary: “Given a context-free grammar G, the Hotz monoid |group] of G is the quotient of the free monoid [group] on the alphabet by the relations defined by the productions. We  ...  Since every semidiscrete context-free language is the image of a strictly bounded one under a rational function, every semidiscrete context-free language must be iterative.  ... 
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Polynomial closure of group languages and open sets of the Hall topology

Jean-Eric Pin
<span title="">1996</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;
Therefore, the syntactic monoid of L, which is a finite group, separates u and v.  ...  and extended to the case of free monoids by Reutenauer [ 191. The group languages form a basis for this topology, that is, the open sets are finite or infinite unions of group languages.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0304-3975(96)00120-x">doi:10.1016/s0304-3975(96)00120-x</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/qjg4atyk7neltez2b55foqlnim">fatcat:qjg4atyk7neltez2b55foqlnim</a> </span>
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Page 4702 of Mathematical Reviews Vol. , Issue 81K [page]

<span title="">1981</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;
The variety approach ha _——-Eime been used by Straubing and Thérien to characterize families of Summ languages whose syntactic monoids contain only solvable group, | ‘Thee Other examples of recently studied  ...  Based on strict | 400 deterministic context-free grammars and LL(k) grammars a new that class of grammars—the partitioned LL(k) (‘PLL(k)’) grammars— are defined.  ... 
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Page 5115 of Mathematical Reviews Vol. , Issue 911 [page]

<span title="">1991</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;
Let V(H) denote the family of finite monoids whose idempotents commute and all of whose groups are in H.  ...  The second chapter deals with regulated rewriting on CF (context free) grammars, where the applications of the CF core productions are regulated by mechanisms such as prescribing sequences of productions  ... 
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Page 1040 of Mathematical Reviews Vol. , Issue 92b [page]

<span title="">1992</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;
The objects dealt with in this book are languages, that is, subsets of the free monoid X*. The main emphasis is on the study of codes and of disjunctive languages.  ...  B. (2-KIEV) Finite automata over the direct product of free semigroups and groups, and languages. (Russian.  ... 
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Polynomial closure of group languages and open sets of the Hall topology [chapter]

Jean -Eric Pin
<span title="">1994</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;
Then d is a distance (in fact an ultrametric distance) which de nes a topology on A , called the pro nite group topology of the free monoid.  ...  Therefore, the syntactic monoid of L, which is a nite group, separates u and v.  ... 
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Algebraic recognizability of languages [article]

Pascal Weil
<span title="2006-09-19">2006</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Recognizable languages of finite words are part of every computer science cursus, and they are routinely described as a cornerstone for applications and for theory.  ...  Context-free languages are defined by context-free grammars, which can be viewed, with a more algebraic mindset, as finite systems of polynomial equations of the form x i = p(x) (1 ≤ i ≤ n) where x = (  ...  In particular, not all context-free languages are recognizable.  ... 
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