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The Intersection Problem for Finite Monoids [article]

Lukas Fleischer, Manfred Kufleitner
2018 arXiv   pre-print
We investigate the intersection problem for finite monoids, which asks for a given set of regular languages, represented by recognizing morphisms to finite monoids from a variety V, whether there exists  ...  We also show that the problem is log-space reducible to the intersection problem for deterministic finite automata (DFA) and that a variant of the problem is log-space reducible to the membership problem  ...  For a variety of finite monoids V, the intersection problem for V is defined as follows.  ... 
arXiv:1711.08717v2 fatcat:upia2zg5q5hezpexhs4lkfd7uu

The Intersection Problem for Finite Monoids

Lukas Fleischer, Manfred Kufleitner
unpublished
We investigate the intersection problem for finite monoids, which asks for a given set of regular languages, represented by recognizing morphisms to finite monoids from a variety V, whether there exists  ...  We also show that the problem is log-space reducible to the intersection problem for deterministic finite automata (DFA) and that a variant of the problem is log-space reducible to the membership problem  ...  For a variety of finite monoids V, the intersection problem for V is defined as follows.  ... 
fatcat:ndajcktyrfan5oedmjyckmaqku

The Intersection Problem for Finite Semigroups [chapter]

Lukas Fleischer
2018 Lecture Notes in Computer Science  
We also establish connections to the monoid variant of the problem.  ...  We investigate the intersection problem for finite semigroups, which asks for a given set of regular languages, represented by recognizing morphisms to finite semigroups, whether there exists a word contained  ...  I would like to thank the anonymous referees of the conference version of this paper for providing helpful comments.  ... 
doi:10.1007/978-3-319-98654-8_26 fatcat:cuvjq6g5ejhthigra5xl6k3bmm

An automata-theoretic approach to the study of the intersection of two submonoids of a free monoid

Laura Giambruno, Antonio Restivo
2008 RAIRO - Theoretical Informatics and Applications  
We investigate the intersection of two finitely generated submonoids of the free monoid on a finite alphabet.  ...  In a more general setting, for an arbitrary number of generators, we prove that if H and K are two finitely generated submonoids generated by prefix sets such that the product automaton associated to H  ...  This last result suggested us to propose the problem of Hanna Neumann for finitely generated submonoids of a free monoid, in the case that their intersection is finitely generated.  ... 
doi:10.1051/ita:2008014 fatcat:6dybvwnyhjbatcqelkmaw64ify

On the rational subset problem for groups [article]

Mark Kambites, Pedro V. Silva (Universidade do Porto), Benjamin Steinberg
2006 arXiv   pre-print
We use language theory to study the rational subset problem for groups and monoids.  ...  We prove further that the problem is decidable for a direct product of a group G with a monoid M if and only if membership is uniformly decidable for G-automata subsets of M.  ...  Acknowledgements The authors would like to thank Stuart Margolis and Friedrich Otto for some helpful conversations.  ... 
arXiv:math/0602454v1 fatcat:u6jaiivfbfachefmygc5wy22ky

On the rational subset problem for groups

Mark Kambites, Pedro V. Silva, Benjamin Steinberg
2007 Journal of Algebra  
We use language theory to study the rational subset problem for groups and monoids.  ...  We prove further that the problem is decidable for a direct product of a group G with a monoid M if and only if membership is uniformly decidable for G-automaton subsets of M.  ...  Acknowledgments The authors thank Stuart Margolis and Friedrich Otto for some helpful conversations.  ... 
doi:10.1016/j.jalgebra.2006.05.020 fatcat:j5f4nz7afvdqnea23e243f22ru

Errata to "Formations of Monoids, Congruences, and Formal Languages"

Adolfo Ballester-Bolinches, Enric Cosme-Llópez, Ramon Esteban-Romero, Jan Rutten
2016 Scientific Annals of Computer Science  
In the proof of [1, Proposition 5], for the case of subdirect products, the set B does not necessarily generate the monoid M .  ...  In order to solve this problem and obtain an Eilenberglike theorem, we need to restrict ourselves to finite-index congruences and regular languages.  ...  The Eilenberg-like theorem for monoids and congruences ([1, Theorem 6]) still holds for the non-finitary case.  ... 
doi:10.7561/sacs.2016.1.123 fatcat:5c3cnsplojbkvl7sdcjs4ixoc4

Page 1063 of Mathematical Reviews Vol. , Issue 88b [page]

1988 Mathematical Reviews  
This result also gives a partial answer to the equivalence problem for a finite union of classes specified by finite, perfect systems of relations.  ...  Summary: “Any finitely generated commutative monoid has a pre- sentation by a finite Noetherian confluent semi-Thue system over a free monoid.” 88b:68105 68Q45 Guo, Yu Qi (PRC-LAN) The ultimate periodicity  ... 

Page 2141 of Mathematical Reviews Vol. , Issue 97D [page]

1997 Mathematical Reviews  
While each monoid (finite monoid) is iso- morphic to the endomorphism monoid of a graph (finite graph), the monoid of strong endomorphisms of a finite graph is always regular.  ...  Two problems of this type include the problem of finding a placement of n non-attacking queens on an n x n chessboard and the problem of determining the minimum number of queens which are necessary to  ... 

The complexity of intersecting finite automata having few final states

Michael Blondin, Andreas Krebs, Pierre McKenzie
2014 Computational Complexity  
The problem of determining whether several finite automata accept a word in common is closely related to the well-studied membership problem in transformation monoids.  ...  For automata with two final states, we show the problem to be ⊕L-complete or NP-complete according to whether a nontrivial monoid other than a direct product of cyclic groups of order 2 is allowed in the  ...  Acknowledgements We thank the referees for helpful comments and for pointing out the need to relax the labelling of the elements transported in the definition of the PT(X) problem.  ... 
doi:10.1007/s00037-014-0089-9 fatcat:tu52mgvwyvbmroeuduqszzuqmy

The Complexity of Intersecting Finite Automata Having Few Final States [chapter]

Michael Blondin, Pierre McKenzie
2012 Lecture Notes in Computer Science  
The problem of determining whether several finite automata accept a word in common is closely related to the well-studied membership problem in transformation monoids.  ...  For automata with two final states, we show the problem to be ⊕L-complete or NP-complete according to whether a nontrivial monoid other than a direct product of cyclic groups of order 2 is allowed in the  ...  Acknowledgements We thank the referees for helpful comments and for pointing out the need to relax the labelling of the elements transported in the definition of the PT(X) problem.  ... 
doi:10.1007/978-3-642-30642-6_4 fatcat:sb27c6n5jfch7eixftbyqukoyi

Unique Decipherability in the Monoid of Languages: An Application of Rational Relations [chapter]

Christian Choffrut, Juhani Karhumäki
2009 Lecture Notes in Computer Science  
We attack the problem of deciding whether a finite collection of finite languages is a code, that is, possesses the unique decipherability property in the monoid of finite languages.  ...  The case of unary languages is one of them and as a consequence, we show how to decide for two given finite subsets of nonnegative integers, whether they are the n-th root of a common set, for some n ≥  ...  Also, since the commutative image of a rational subset of a free monoid is a semilinear set of N m , Theorem 4 also holds for a finite collections of rational, not only finite, languages of a free monoid  ... 
doi:10.1007/978-3-642-03351-3_9 fatcat:25br2xdihrdkhlm3pade2r2yga

Unique Decipherability in the Monoid of Languages: An Application of Rational Relations

Christian Choffrut, Juhani Karhumäki
2011 Theory of Computing Systems  
We attack the problem of deciding whether a finite collection of finite languages is a code, that is, possesses the unique decipherability property in the monoid of finite languages.  ...  The case of unary languages is one of them and as a consequence, we show how to decide for two given finite subsets of nonnegative integers, whether they are the n-th root of a common set, for some n ≥  ...  Also, since the commutative image of a rational subset of a free monoid is a semilinear set of N m , Theorem 4 also holds for a finite collections of rational, not only finite, languages of a free monoid  ... 
doi:10.1007/s00224-011-9324-9 fatcat:n3xh6g65rndnjiub74cejilzhu

On Decidability of Intermediate Levels of Concatenation Hierarchies [chapter]

Jorge Almeida, Jana Bartoňová, Ondřej Klíma, Michal Kunc
2015 Lecture Notes in Computer Science  
In terms of the quantifier-alternation hierarchy of sentences in the first-order logic of finite words, this means that decidability of (definability in) the Σn fragment implies that of ∆n+1.  ...  It is proved that in every concatenation hierarchy of regular languages, decidability of one of its half levels, obtained by polynomial closure, implies decidability of the intersection of the following  ...  For every pseudovariety of ordered monoids V, the membership problem for the pseudovariety V M can be reduced in polynomial time to the membership problem for V.  ... 
doi:10.1007/978-3-319-21500-6_4 fatcat:tyhp3ovqsbafzez37kkxjvskme

Two-letter group codes that preserve aperiodicity of inverse finite automata

Jean-Camille Birget, Stuart W. Margolis
2007 Semigroup Forum  
The membership problem for 3-generated inverse monoids is PSPACE-complete.  ...  As an application we show that the following problems are PSPACE-complete for two-letter alphabets (this was previously known for large enough finite alphabets): The intersection-emptiness problem for  ...  Theorem 3. 2 2 The membership problem for the class of finite inverse monoids is PSPACE-complete.  ... 
doi:10.1007/s00233-007-9024-6 fatcat:5p4ngj75g5dvfpbhuamofir7vy
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