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Page 1195 of Mathematical Reviews Vol. 36, Issue 5
[page]
1968
Mathematical Reviews
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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
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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
2002
Journal of the ACM
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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]
2004
Lecture Notes in Computer Science
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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]
2006
arXiv
pre-print
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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
1993
Transactions of the American Mathematical Society
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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
1993
Transactions of the American Mathematical Society
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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
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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
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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
2009
Journal of the London Mathematical Society
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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
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(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
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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
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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
2015
Information and Computation
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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
1991
Journal of Algebra
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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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