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Syntactic Complexity of Star-Free Languages
[article]

2011
*
arXiv
*
pre-print

We conjecture that this bound is also an upper bound on the

arXiv:1109.3381v1
fatcat:xdoe2qmlpjcq5j4y7s3jc7dhnm
*syntactic**complexity**of**star*-*free**languages*. ... We study the*syntactic**complexity**of**star*-*free*regular*languages*, that is,*languages*that can be constructed from finite*languages*using union, complement and concatenation. ... The figures in bold type are tight bounds verified using GAP [7] , by enumerating aperiodic subsemigroups*of*T Q . The asterisk * indicates that the bound is already tight for a smaller alphabet. ...##
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Towards a Theory of Complexity of Regular Languages
[article]

2017
*
arXiv
*
pre-print

In addition to the quotient

arXiv:1702.05024v1
fatcat:gzkyubh2ireizdsuu6fpqy6ece
*complexity**of*the*language*-- which is the number*of*its (left) quotients, and is the same as its state*complexity*-- we also consider the size*of*its*syntactic*semigroup and ... We then turn to the study*of*the quotient/state*complexity**of*common operations on regular*languages*: reversal, (Kleene)*star*, product (concatenation) and boolean operations. ...*Syntactic**complexities*for several subclasses*of**star*-*free**languages*have been found: 1. ...##
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A Quantum Query Complexity Trichotomy for Regular Languages
[article]

2019
*
arXiv
*
pre-print

The heart

arXiv:1812.04219v3
fatcat:zo3oe6f64bfgrmhqsvxu3m4qqy
*of*the classification theorem is an explicit quantum algorithm which decides membership in any*star*-*free**language*in ~O(sqrt n) time. ... Thus, we view the algorithm for*star*-*free**languages*as a nontrivial generalization*of*Grover's algorithm which extends the quantum quadratic speedup to a much wider range*of*string-processing algorithms ... Finally, we are aware*of*one more result on the*complexity**of**star*-*free**languages*prior to our work. ...##
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Complexity of Suffix-Free Regular Languages
[article]

2016
*
arXiv
*
pre-print

It is known that there exist such most

arXiv:1504.05159v4
fatcat:jivxp23gwrb3xe6mrlnh3qqnoq
*complex*streams in the*class**of*regular*languages*, in the*class**of*prefix-*free**languages*, and also in the*classes**of*right, left, and two-sided ideals. ... We study various*complexity*properties*of*suffix-*free*regular*languages*. ... Secondly, all the bounds for common operations -except reversal, which misses the bound by one state -are also met by*star*-*free**languages*[13] , where the*class**of**star*-*free**languages*is the smallest ...##
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Logic Meets Algebra: the Case of Regular Languages

2007
*
Logical Methods in Computer Science
*

Since the work

doi:10.2168/lmcs-3(1:4)2007
fatcat:oylwgpnv2jb6jjemhloczatozi
*of*Buchi, regular*languages*have been classified according to their descriptive*complexity*, i.e. the type*of*logical formalism required to define them. ... We also explain the impact*of*these connections on circuit*complexity*theory. ... Acknowledgements: We want to thank the anonymous referees for their suggestions to improve the readability*of*the paper. We also want to thank Luc Segoufin and Jean-Éric Pin for useful discussions. ...##
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Complexity of Suffix-Free Regular Languages
[chapter]

2015
*
Lecture Notes in Computer Science
*

We study various

doi:10.1007/978-3-319-22177-9_12
fatcat:sducrq3fi5aclpyzddrtwmwqfy
*complexity*properties*of*suffix-*free*regular*languages*. ... In contrast to this, we prove that there does not exist a most*complex*sequence in the*class**of*suffix-*free*regular*languages*. ... Acknowledgments This work was supported by the Natural Sciences and Engineering Research Council*of*Canada (NSERC) grant No. ...##
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Syntactic Complexity of Prefix-, Suffix-, Bifix-, and Factor-Free Regular Languages
[article]

2011
*
arXiv
*
pre-print

The

arXiv:1103.2986v2
fatcat:nsm64qkydjd4jdxlifkplr5ywa
*syntactic**complexity**of*a subclass*of*the*class**of*regular*languages*is the maximal*syntactic**complexity**of**languages*in that*class*, taken as a function*of*the state*complexity*n*of*these*languages*... We study the*syntactic**complexity**of*prefix-, suffix-, bifix-, and factor-*free*regular*languages*. We prove that n^n-2 is a tight upper bound for prefix-*free*regular*languages*. ... In 2010 Brzozowski and Ye [3] examined the*syntactic**complexity**of*ideal and closed regular*languages*, and in 2011 Brzozowski and Li [6] studied the*syntactic**complexity**of**star*-*free**languages*. ...##
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SYNTACTIC COMPLEXITY OF ℛ- AND 𝒥-TRIVIAL REGULAR LANGUAGES

2014
*
International Journal of Foundations of Computer Science
*

The

doi:10.1142/s0129054114400097
fatcat:levq7nx7rffavgmfsgsy44uocu
*syntactic**complexity**of*a subclass*of*the*class**of*regular*languages*is the maximal cardinality*of**syntactic*semigroups*of**languages*in that*class*, taken as a function*of*the state*complexity*n*of*... are tight upper bounds for the*syntactic**complexity**of*Rand J -trivial regular*languages*, respectively. ... H-trivial regular*languages*are exactly the*star*-*free**languages*[14, 17] , and L-, R-, and J -trivial regular*languages*are all subclasses*of*the*class**of**star*-*free**languages*. ...##
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Syntactic complexity of prefix-, suffix-, bifix-, and factor-free regular languages

2012
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Theoretical Computer Science
*

The

doi:10.1016/j.tcs.2012.04.011
fatcat:266x5rjnbzh5xdkhkeeuurezpy
*syntactic**complexity**of*a subclass*of*the*class**of*regular*languages*is the maximal*syntactic**complexity**of**languages*in that*class*, taken as a function*of*the state*complexity*n*of*these*languages*... The*syntactic**complexity**of*a regular*language*is the cardinality*of*its*syntactic*semigroup. ... In 2010, Brzozowski and Ye [6] examined the*syntactic**complexity**of*ideal and closed regular*languages*, and in 2011, Brzozowski and Li [5] studied the*syntactic**complexity**of**star*-*free**languages*. ...##
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Most Complex Non-Returning Regular Languages

2019
*
International Journal of Foundations of Computer Science
*

We find the maximal state

doi:10.1142/s0129054119400239
fatcat:ia5qkbf75bd7jaummthegmbnw4
*complexities**of*atoms*of*non-returning*languages*. ... These five witnesses use a total*of**six*different transformations. ... They pointed out that several interesting subclasses*of*regular*languages*have the non-returning property; these subclasses include the*class**of*suffix-*free**languages*(suffix codes) and its subclasses ...##
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Typed and unambiguous pattern matching on strings using regular expressions

2010
*
Proceedings of the 12th international ACM SIGPLAN symposium on Principles and practice of declarative programming - PPDP '10
*

We also show how pattern matching can be integrated into statically typed programming

doi:10.1145/1836089.1836120
dblp:conf/ppdp/BrabrandT10
fatcat:6fdrk6nd5ndxdmr6vv2z42byue
*languages*for deconstructing strings and reproducing typed and structured values. ... The analysis is capable*of*pinpointing all ambiguities in terms*of*the structure*of*the regular expression and report shortest ambiguous strings. ... We would also like to thank the reviewers*of*PPDP 2010 for their comments, suggestions, and bibliographical indications. ...##
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Semigroups and languages of dot-depth two

1988
*
Theoretical Computer Science
*

This paper is a contribution to the problem

doi:10.1016/0304-3975(88)90034-5
fatcat:22qveyh25naz5a3iz2wtxeq66m
*of*effectively determining the dot-depth*of*a*star*-*free**language*, a problem concerning forma1*languages*that has close connections to semigroup theory and mathematical ... I conjecture an effective criterion, based on the*syntactic*monoid*of*the*language*, for determining whether a given*language*has dot-depth two, and prove the conjecture in the case*of**languages*over an ... (The analogous result holds for the*star*-*free**languages*in A+: Lc_ A+ is*star*-*free*if and only if its*syntactic*semigroup S(L) is finite and aperiodic.) ...##
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Duality and Recognition
[chapter]

2011
*
Lecture Notes in Computer Science
*

The fact that one can associate a finite monoid with universal properties to each

doi:10.1007/978-3-642-22993-0_3
fatcat:wypwkdeib5gvxaibobuobdlhui
*language*recognised by an automaton is central to the solution*of*many practical and theoretical problems in automata theory ... The*class**of**star*-*free**languages*is axiomatised by x ω = x ω+1 with the interpretation*of*x ranging over all profinite words. ... Thus natural subclasses arise as the*classes**of**languages*corresponding to fragments*of*monadic second order logic. The classical example is that*of*the*star*-*free**languages*. ...##
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A Survey on Operational State Complexity
[article]

2015
*
arXiv
*
pre-print

Operational state

arXiv:1509.03254v1
fatcat:oxleg7kkvvezxoqgscdnlghzvu
*complexity*is the study*of*the state*complexity**of*operations over*languages*. ... Descriptional*complexity*is the study*of*the conciseness*of*the various models representing formal*languages*. ...*Star*-*free**Languages**Star*-*free**languages*are the smallest*class*containing the finite*languages*and closed under Boolean operations and catenation. ...##
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Most Complex Regular Ideal Languages
[article]

2016
*
arXiv
*
pre-print

In that sense, these ideals are "most

arXiv:1511.00157v3
fatcat:5ssf2cwvf5fnhpv3feucvq2sau
*complex*"*languages*in their*classes*, or "universal witnesses" to the*complexity**of*the various operations. ... the following measures*of**complexity*: the size*of*the*syntactic*semigroup, the quotient*complexities**of*the left quotients*of*L_n, the number*of*atoms (intersections*of*complemented and uncomplemented ... Our main new result is a demonstration that these sequences are in fact most*complex*. It has been shown in [11] that a most*complex*sequence does not exist for the*class**of*suffix-*free**languages*. ...
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