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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

2015
*
Scientific Annals of Computer Science
*

The main goal in this paper is

doi:10.7561/sacs.2015.2.171
fatcat:hh7gcph3ivg6pi2hibuxzrg55e
*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. ...##
###
Timed regular expressions

2002
*
Journal of the ACM
*

In this paper we define timed regular expressions,

doi:10.1145/506147.506151
fatcat:wy2cjdv5dbbodaums2utyxcoye
*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). ...##
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Algebraic Recognizability of Languages
[chapter]

2004
*
Lecture Notes in Computer Science
*

into finite

doi:10.1007/978-3-540-28629-5_8
fatcat:5el7wd3umvgdzhw4dxukeugoci
*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 ...##
###
Algebraic recognizability of languages
[article]

2006
*
arXiv
*
pre-print

Recognizable languages

arXiv:cs/0609110v1
fatcat:2fnhr3gu5rdbbdugq76cqfvl4y
*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 ...##
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Inverse monoids, trees and context-free languages

1993
*
Transactions of the American Mathematical Society
*

This paper is concerned

doi:10.1090/s0002-9947-1993-1073775-x
fatcat:5jhonep63verdc7hnzd4kxsqgm
*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*. ...##
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Inverse Monoids, Trees, and Context-Free Languages

1993
*
Transactions of the American Mathematical Society
*

This paper is concerned

doi:10.2307/2154268
fatcat:r7egjg6ek5f3fho5jwj6xherha
*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*. ...##
###
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*). ...##
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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.) ...##
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Rational codes and free profinite monoids

2009
*
Journal of the London Mathematical Society
*

More generally, our results apply

doi:10.1112/jlms/jdn083
fatcat:k4naaoqwtbfsno5cculnokosua
*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. ...##
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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**}. ...##
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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. ...

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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*.” ...

##
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On labeled birooted tree languages: Algebras, automata and logic

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. ...

##
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Topologies for the free monoid

1991
*
Journal of Algebra
*

It is well known that every

doi:10.1016/0021-8693(91)90094-o
fatcat:grzyzsgcvvhlbken374suw6to4
*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*. ...
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