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Page 1195 of Mathematical Reviews Vol. 36, Issue 5 [page]

1968 Mathematical Reviews  
M. 6235 Congruence separation of subsets of a monoid with appli- cations to automata. Math. Systems Theory 1 (1967), 315-324.  ...  The set @,,’ of all - separating congruences on F is a lower semi-lattice with respect to the partial ordering of congruence inclusion.  ... 

Formations of Monoids, Congruences, and Formal Languages

Adolfo Ballester-Bolinches, Enric Cosme-Llópez, Ramon Esteban-Romero, Jan Rutten
2015 Scientific Annals of Computer Science  
The main goal in this paper is to use a dual equivalence in automata theory started in [25] and developed in [3] to prove a general version of the Eilenberg-type theorem presented in [4] .  ...  We relate our work to other results in the field and we include applications to non-r-disjunctive languages, Reiterman's equational description of pseudovarieties and varieties of monoids.  ...  Acknowledgements The authors gratefully acknowledge various discussions with Jean-Éric Pin.  ... 
doi:10.7561/sacs.2015.2.171 fatcat:hh7gcph3ivg6pi2hibuxzrg55e

Timed regular expressions

Eugene Asarin, Paul Caspi, Oded Maler
2002 Journal of the ACM  
In this paper we define timed regular expressions, a formalism for specifying discrete behaviors augmented with timing information, and prove that its expressive power is equivalent to the timed automata  ...  This result is the timed analogue of Kleene Theorem and, similarly to that result, the hard part in the proof is the translation from automata to expressions.  ...  Recognizability of a subset L of a monoid M can be defined in automaton-free terms. Let ∼ be syntactic right congruence associated with L, namely u ∼ v iff ∀w ∈ M(u · w ∈ L ⇐⇒ v · w ∈ L).  ... 
doi:10.1145/506147.506151 fatcat:wy2cjdv5dbbodaums2utyxcoye

Algebraic Recognizability of Languages [chapter]

Pascal Weil
2004 Lecture Notes in Computer Science  
into finite monoids, or equivalently, of finite-index monoid congruences.  ...  It can be approached from several angles: recognizability by automata, recognizability by finite monoids or finite-index congruences, rational expressions, monadic second order definability.  ...  moreover, they introduced a simple model of automata for subsets of SP B(A), whose power is equivalent to recognizability and to MSO-definability [35] .É sik and Németh's automata can also be defined  ... 
doi:10.1007/978-3-540-28629-5_8 fatcat:5el7wd3umvgdzhw4dxukeugoci

Algebraic recognizability of languages [article]

Pascal Weil
2006 arXiv   pre-print
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.  ...  We would like to briefly explore why that is, and how this word-related notion extends to more complex models, such as those developed for modeling distributed or timed behaviors.  ...  moreover, they introduced a simple model of automata for subsets of SP B(A), whose power is equivalent to recognizability and to MSO-definability [35] .É sik and Németh's automata can also be defined  ... 
arXiv:cs/0609110v1 fatcat:2fnhr3gu5rdbbdugq76cqfvl4y

Inverse monoids, trees and context-free languages

Stuart W. Margolis, John C. Meakin
1993 Transactions of the American Mathematical Society  
This paper is concerned with a study of inverse monoids presented by a set X subject to relations of the form e¡ = f¡, i € I, where e¡ and f¡ are Dyck words, i.e. idempotents of the free inverse monoid  ...  Some connections with the theory of rational subsets of the free group and the theory of context-free languages are explored.  ...  Clearly SIM(X) has a zero, the "empty mapping" from the empty subset of X to itself. It is easy to see that SIM(A') is an inverse monoid with a~x : R(a) -, D(a) as the inverse of the bijection a.  ... 
doi:10.1090/s0002-9947-1993-1073775-x fatcat:5jhonep63verdc7hnzd4kxsqgm

Inverse Monoids, Trees, and Context-Free Languages

Stuart W. Margolis, John C. Meakin
1993 Transactions of the American Mathematical Society  
This paper is concerned with a study of inverse monoids presented by a set X subject to relations of the form e¡ = f¡, i € I, where e¡ and f¡ are Dyck words, i.e. idempotents of the free inverse monoid  ...  Some connections with the theory of rational subsets of the free group and the theory of context-free languages are explored.  ...  Clearly SIM(X) has a zero, the "empty mapping" from the empty subset of X to itself. It is easy to see that SIM(A') is an inverse monoid with a~x : R(a) -, D(a) as the inverse of the bijection a.  ... 
doi:10.2307/2154268 fatcat:r7egjg6ek5f3fho5jwj6xherha

Page 6861 of Mathematical Reviews Vol. , Issue 2004i [page]

2004 Mathematical Reviews  
Let S be a commutative, cancellative torsion-free monoid, written additively, with quotient group G. An overmonoid of S is a sub- monoid of G containing S.  ...  The author gives the definitions of module systems, r-module (those subsets of D satisfying J, = J) and r-monoid (the r-modules which are also monoids).  ... 

Page 2184 of Mathematical Reviews Vol. , Issue 80F [page]

1980 Mathematical Reviews  
Proposition 3: Let A and B be subsets of M and let A be closed with respect to a congruence p on M. If B"=A for some n, then there exists a set C, closed with respect to p, such that C"=A.  ...  (m(A) is the index of the minimal congruence p on M such that A is closed with respect to p, i.e., A is the union of some p-classes.)  ... 

Rational codes and free profinite monoids

Jorge Almeida, Benjamin Steinberg
2009 Journal of the London Mathematical Society  
More generally, our results apply to free pro-H monoids for H an extension-closed pseudovariety of groups.  ...  Clopen submonoids of free profinite monoids need not be finitely generated nor free.  ...  Let V be a pseudovariety of monoids. A monoid M is said to be residually V if it has enough homomorphisms to elements of V to separate points.  ... 
doi:10.1112/jlms/jdn083 fatcat:k4naaoqwtbfsno5cculnokosua

Page 6721 of Mathematical Reviews Vol. , Issue 97K [page]

1997 Mathematical Reviews  
(If / is a set and Z/ is the direct product of |/| copies of Z with projection maps 7; (i € J), then a subset X of Z’ is summable if for each j € 1, 2;(x)=0 for all but a finite number of x in X.)  ...  Let A* be the free semigroup over a finite set A with at least two elements and consider the congruence «,,,, generated by nm = {(v",v"*"): v € A*}.  ... 

Page 3643 of Mathematical Reviews Vol. , Issue 93g [page]

1993 Mathematical Reviews  
A method of a local approach to a monoid M of Lie type, via a special class of universal monoids with three or four J-classes, is presented in order to discuss the linear representations of M and their  ...  For any such pair (G,/), the author constructs a finite matrix D;(G) with elements equal to 0 or 1. Let R be a ring. Then 2(R) is a subset of nonnegative integers defined as follows.  ... 

Page 40 of Mathematical Reviews Vol. , Issue 2000j [page]

2000 Mathematical Reviews  
to E; the greatest idempotent separating congruence on T¢ is the equality relation; and for any inverse semigroup S whose subsemilattice of idempotents is E there is an idempotent separating homomor-  ...  It is also proved that a semigroup S is a normal band of unipotent monoids if and only if S is a strong semilattice of Rees matrix semigroups over unipotent monoids.”  ... 

On labeled birooted tree languages: Algebras, automata and logic

David Janin
2015 Information and Computation  
With an aim to developing expressive language theoretical tools applicable to inverse semigroup languages, that is, subsets of inverse semigroups, this paper explores the language theory of finite labeled  ...  To this purpose, we define a notion of finite state birooted tree automata that simply extends finite state word automata semantics.  ...  Acknowledgment The author wishes to express his gratitude to the anonymous referees for providing many helpful comments on earlier versions of this work.  ... 
doi:10.1016/j.ic.2014.12.016 fatcat:gg4tea6z3jffxbx5jqcxky4rxe

Topologies for the free monoid

J.E Pin
1991 Journal of Algebra  
It is well known that every subset L of the free monoid A* defines in a natural way a congruence on A*, called the syntactic congruence.  ...  The subsets of A* for which this congruence is of finite index are called l Supported by the PRC Mathdmatiques et Informatique.  ...  It is well known that every subset L of the free monoid A* defines in a natural way a congruence on A*, called the syntactic congruence.  ... 
doi:10.1016/0021-8693(91)90094-o fatcat:grzyzsgcvvhlbken374suw6to4
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