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Page 3206 of Mathematical Reviews Vol. , Issue 98E [page]

1998 Mathematical Reviews  
In fact, we show that the Knuth-Bendix completion procedure always terminates when ap- plied to prefix-rewriting systems on virtually free presentations of context-free groups.  ...  “It is known that the generalized word problem for context-free groups is decidable. Here we show how prefix-rewriting systems can be used to solve this problem.  ... 

Page 6990 of Mathematical Reviews Vol. , Issue 96k [page]

1996 Mathematical Reviews  
group topology or with respect to one of the p-adic topologies.  ...  Finally, we determine the structure of a cohesive prefix code that is a right semaphore code.” 96k:68114 68Q45 20M35 Kari, Lila (3-WON; London, ON); Thierrin, Gabriel (3-WON; London, ON) k-insertion and  ... 

Non-finitely Generated Maximal Subgroups of Context-free Monoids [article]

Carl-Fredrik Nyberg-Brodda
2021 arXiv   pre-print
and context-free groups.  ...  This answers a question of Brough, Cain & Pfeiffer on whether the group of units of a context-free monoid is always finitely generated, and highlights some of the contrasts between context-free monoids  ...  One can regard Π 2 as the result of a certain procedure: start with a family of pairwise isomorphic groups C 2,i = Mon x i | x 2 i = 1 , each of which admits a context-free complete monadic rewriting system  ... 
arXiv:2107.12861v2 fatcat:qou5oap2c5hpjgfchbcjlbgmam

Relating rewriting techniques on monoids and rings: congruences on monoids and ideals in monoid rings

Klaus Madlener, Birgit Reinert
1998 Theoretical Computer Science  
For several classes of finitely presented groups we show explicitly how Grabner basis methods are related to existing solutions of the subgroup problem that are based on rewriting methods.  ...  The aim of this paper is to show how congruences on monoids and groups can be characterized by ideals in the corresponding monoid and group rings.  ...  We both thank Andrea Sattler-Klein, Teo Mora, Paliath Narendran and Friedrich Otto for valuable discussions on parts of this paper.  ... 
doi:10.1016/s0304-3975(98)00077-2 fatcat:j5phzlmmqzeutm2wuviychbloe

Local similarity groups with context-free co-word problem [article]

Daniel Farley
2014 arXiv   pre-print
A current conjecture, based originally on a conjecture of Lehnert and modified into its current form by Bleak, Matucci, and Neuhöffer, says that Thompson's group V is a universal group with context-free  ...  In other words, it is conjectured that a group has a context-free co-word problem exactly if it is a finitely generated subgroup of V.  ...  The (non-deterministic) context-free languages are not closed under taking complements, however, so groups with context-free co-word problem are not (a priori, at least) the same as groups with context-free  ... 
arXiv:1406.4590v1 fatcat:la3lmiadtzh4llqvzdwpmimarm

Page 3476 of Mathematical Reviews Vol. , Issue 88g [page]

1988 Mathematical Reviews  
Motivated by prefix, suffix, and embedding orders on free monoids, basic properties of general (left, right) compatible partial orders on free monoids, in particular their corresponding antichains, are  ...  Let A be a finite alphabet and denote by A* the free monoid on A. Two metrics are defined on A*.  ... 

Autostackability of Thompson's group F [article]

Nathan Corwin, Gili Golan, Susan Hermiller, Ashley Johnson, Zoran Sunic
2018 arXiv   pre-print
We show that the group F admits a natural extension of these two properties, namely autostackability, and we give an explicit bounded regular convergent prefix-rewriting system for F.  ...  The word problem for Thompson's group F has a solution, but it remains unknown whether F is automatic or has a finite or regular convergent (terminating and confluent) rewriting system.  ...  Lemma for regular languages [13, Lemma 3.1], nor the Pumping Lemma for context-free languages [13, Lemma 6.1], and so the rewriting system Σ is neither (synchronously) regular nor context-free.  ... 
arXiv:1811.11691v1 fatcat:wpguyl4y7zdf3gfrq4ixs7e7f4

A word-hyperbolic special monoid with undecidable Diophantine problem [article]

Carl-Fredrik Nyberg-Brodda
2022 arXiv   pre-print
In this note, we give a simple example of a context-free, word-hyperbolic, finitely presented, special monoid M with trivial group of units, and such that the Diophantine problem is undecidable in M.  ...  This answers two questions asked by Garreta Gray in 2019, and shows that the decidability of the Diophantine problem in hyperbolic groups, as proved by Dahmani Guirardel, does not generalise to word-hyperbolic  ...  The free monoid on a finite set A is denoted by A * , and the free semigroup is denoted by A + .  ... 
arXiv:2205.01056v1 fatcat:gzrdz6it4fgttany6e46f27fri

Page 3873 of Mathematical Reviews Vol. , Issue 98F [page]

1998 Mathematical Reviews  
These languages are neither context-free nor DOL languages, but the inclusion (implicitly, the equivalence) problem is decidable, as are other problems.  ...  It is shown that both regular and context-free languages can be represented by certain types of algebra grammars.” 98F:68151 68Q45 68Q10 68Q42 Bertol, Michael (D-STGT-1; Stuttgart); Diekert, Volker (D-STGT-I  ... 

Markov semigroups, monoids and groups

Alan J. Cain, Victor Maltcev
2014 International journal of algebra and computation  
A group is Markov if it admits a prefix-closed regular language of unique representatives with respect to some generating set, and strongly Markov if it admits such a language of unique minimal-length  ...  A study is made of the interaction of the classes of Markov and strongly Markov semigroups with direct products, free products, and finite-index subsemigroups and extensions.  ...  Since the rewriting system (A, R) is context-free, M is word-hyperbolic by [CM12, Theorem 3.1].  ... 
doi:10.1142/s021819671450026x fatcat:ykvmckxjvbcnffomly24fy7xrm

Cumulative subject index volumes 44–47

1980 Information and Control  
binary codes outside Plotkin range, 47, 85 Griessner, codes meeting: uniqueness respecting nonexistence of, 44, 16 upper, for difference between two entropies, 45, 34 Bounded deterministic languages context-free  ...  , 10 store, real-time: equivalence problem for, 45, 90 indexed pushdown, and deterministic indexed languages, 45, 48 nondeterministic and stochastic, state transition policies for, 46, 135 semigroup, group  ...  -free languages prefix-free: derivatives and quotients of, 45, 229 test sets for bomomorphism equivalence on, 45,273 -free tree languages, Greibach's tree languages contained in, 46, 108 -sensitive  ... 
doi:10.1016/s0019-9958(80)90592-6 fatcat:zwdwzq5kifakzlpgfkl5hog2ra

On the Word Problem for Special Monoids [article]

Carl-Fredrik Nyberg-Brodda
2021 arXiv   pre-print
As a corollary, we prove that it is decidable (in polynomial time) whether a special one-relation monoid has context-free word problem.  ...  We prove that a special monoid has context-free word problem if and only if its group of units is virtually free, giving a full generalisation of the Muller-Schupp theorem.  ...  Gray for valuable feedback (on several iterations of the present article), and Tara Brough for discussions pertaining to Conjecture 2.  ... 
arXiv:2011.09466v3 fatcat:hilp5uxmyjfcjhamvvnwmhnebu

About the descriptive power of certain classes of finite string-rewriting systems

Klaus Madlener, Friedrich Otto
1989 Theoretical Computer Science  
Finite string-rewriting systems can be used to present monoids and groups. In general, these finite presentations do not give much information about the monoids and groups presented.  ...  But also the problems of deciding whether the monoid MR is finite, whether it is commutative, whether it is a free monoid, and whether it is a group are decidable in this situation [18, 541.  ...  for the class of context-free groups [4] .  ... 
doi:10.1016/0304-3975(89)90002-9 fatcat:onterhtqvncyxk34zrcszlhmli

Page 6628 of Mathematical Reviews Vol. , Issue 88m [page]

1988 Mathematical Reviews  
Klaus Madlener (D-KSRL-I) 88m:68027 68Q45 Autebert, Jean-Michel (F-PARIS7-LI); Flajolet, Philippe (F-INRIA); Gabarr6é, Joaquim (E-UPBI) Prefixes of infinite words and ambiguous context-free languages.  ...  Finally, the free product of two rational monoids is rational if and only if the group of units of one of the monoids is trivial. Jean-Eric Pin (Paris) 88m:68025 68Q30 03B48 Asarin, E. A.  ... 

The Reachability Problem over Infinite Graphs [chapter]

Wolfgang Thomas
2009 Lecture Notes in Computer Science  
Our focus is on graphs that are presented in terms of word or tree rewriting systems.  ...  We survey classical and selected recent work on the reachability problem over finitely presented infinite graphs.  ...  Under these conventions, it is known that pushdown graphs with ε-transitions recognize precisely the context-free languages and automatic graphs precisely the context-sensitive languages.  ... 
doi:10.1007/978-3-642-03351-3_2 fatcat:ocehdjg765ejvbzjlb3qshwxve
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