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The Intersection Problem for Finite Monoids
[article]

2018
*
arXiv
*
pre-print

We investigate

arXiv:1711.08717v2
fatcat:upia2zg5q5hezpexhs4lkfd7uu
*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. ...##
###
The Intersection Problem for Finite Monoids

unpublished

We investigate

fatcat:ndajcktyrfan5oedmjyckmaqku
*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. ...##
###
The Intersection Problem for Finite Semigroups
[chapter]

2018
*
Lecture Notes in Computer Science
*

We also establish connections to

doi:10.1007/978-3-319-98654-8_26
fatcat:cuvjq6g5ejhthigra5xl6k3bmm
*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. ...##
###
An automata-theoretic approach to the study of the intersection of two submonoids of a free monoid

2008
*
RAIRO - Theoretical Informatics and Applications
*

We investigate

doi:10.1051/ita:2008014
fatcat:6dybvwnyhjbatcqelkmaw64ify
*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. ...##
###
On the rational subset problem for groups
[article]

2006
*
arXiv
*
pre-print

We use language theory to study

arXiv:math/0602454v1
fatcat:u6jaiivfbfachefmygc5wy22ky
*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. ...##
###
On the rational subset problem for groups

2007
*
Journal of Algebra
*

We use language theory to study

doi:10.1016/j.jalgebra.2006.05.020
fatcat:j5f4nz7afvdqnea23e243f22ru
*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. ...##
###
Errata to "Formations of Monoids, Congruences, and Formal Languages"

2016
*
Scientific Annals of Computer Science
*

In

doi:10.7561/sacs.2016.1.123
fatcat:5c3cnsplojbkvl7sdcjs4ixoc4
*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. ...##
###
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

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*. ...

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

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*. ...

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

2009
*
Lecture Notes in Computer Science
*

We attack

doi:10.1007/978-3-642-03351-3_9
fatcat:25br2xdihrdkhlm3pade2r2yga
*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*...##
###
Unique Decipherability in the Monoid of Languages: An Application of Rational Relations

2011
*
Theory of Computing Systems
*

We attack

doi:10.1007/s00224-011-9324-9
fatcat:n3xh6g65rndnjiub74cejilzhu
*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*...##
###
On Decidability of Intermediate Levels of Concatenation Hierarchies
[chapter]

2015
*
Lecture Notes in Computer Science
*

In terms of

doi:10.1007/978-3-319-21500-6_4
fatcat:tyhp3ovqsbafzez37kkxjvskme
*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. ...##
###
Two-letter group codes that preserve aperiodicity of inverse finite automata

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. ...

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