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Syntactic Complexity of Star-Free Languages [article]

Janusz Brzozowski, Baiyu Li
2011 arXiv   pre-print
We conjecture that this bound is also an upper bound on the 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.  ... 
arXiv:1109.3381v1 fatcat:xdoe2qmlpjcq5j4y7s3jc7dhnm

Towards a Theory of Complexity of Regular Languages [article]

Janusz A. Brzozowski
2017 arXiv   pre-print
In addition to the quotient 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.  ... 
arXiv:1702.05024v1 fatcat:gzkyubh2ireizdsuu6fpqy6ece

A Quantum Query Complexity Trichotomy for Regular Languages [article]

Scott Aaronson, Daniel Grier, Luke Schaeffer
2019 arXiv   pre-print
The heart 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.  ... 
arXiv:1812.04219v3 fatcat:zo3oe6f64bfgrmhqsvxu3m4qqy

Complexity of Suffix-Free Regular Languages [article]

Janusz Brzozowski, Marek Szykuła
2016 arXiv   pre-print
It is known that there exist such most 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  ... 
arXiv:1504.05159v4 fatcat:jivxp23gwrb3xe6mrlnh3qqnoq

Logic Meets Algebra: the Case of Regular Languages

Pascal Tesson, Denis Thérien, Leonid Libkin
2007 Logical Methods in Computer Science  
Since the work 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.  ... 
doi:10.2168/lmcs-3(1:4)2007 fatcat:oylwgpnv2jb6jjemhloczatozi

Complexity of Suffix-Free Regular Languages [chapter]

Janusz Brzozowski, Marek Szykuła
2015 Lecture Notes in Computer Science  
We study various 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.  ... 
doi:10.1007/978-3-319-22177-9_12 fatcat:sducrq3fi5aclpyzddrtwmwqfy

Syntactic Complexity of Prefix-, Suffix-, Bifix-, and Factor-Free Regular Languages [article]

Janusz Brzozowski, Baiyu Li, Yuli Ye
2011 arXiv   pre-print
The 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.  ... 
arXiv:1103.2986v2 fatcat:nsm64qkydjd4jdxlifkplr5ywa

SYNTACTIC COMPLEXITY OF ℛ- AND 𝒥-TRIVIAL REGULAR LANGUAGES

JANUSZ BRZOZOWSKI, BAIYU LI
2014 International Journal of Foundations of Computer Science  
The 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.  ... 
doi:10.1142/s0129054114400097 fatcat:levq7nx7rffavgmfsgsy44uocu

Syntactic complexity of prefix-, suffix-, bifix-, and factor-free regular languages

Janusz Brzozowski, Baiyu Li, Yuli Ye
2012 Theoretical Computer Science  
The 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.  ... 
doi:10.1016/j.tcs.2012.04.011 fatcat:266x5rjnbzh5xdkhkeeuurezpy

Most Complex Non-Returning Regular Languages

Janusz A. Brzozowski, Sylvie Davies
2019 International Journal of Foundations of Computer Science  
We find the maximal state 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  ... 
doi:10.1142/s0129054119400239 fatcat:ia5qkbf75bd7jaummthegmbnw4

Typed and unambiguous pattern matching on strings using regular expressions

Claus Brabrand, Jakob G. Thomsen
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 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.  ... 
doi:10.1145/1836089.1836120 dblp:conf/ppdp/BrabrandT10 fatcat:6fdrk6nd5ndxdmr6vv2z42byue

Semigroups and languages of dot-depth two

Howard Straubing
1988 Theoretical Computer Science  
This paper is a contribution to the problem 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.)  ... 
doi:10.1016/0304-3975(88)90034-5 fatcat:22qveyh25naz5a3iz2wtxeq66m

Duality and Recognition [chapter]

Mai Gehrke
2011 Lecture Notes in Computer Science  
The fact that one can associate a finite monoid with universal properties to each 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.  ... 
doi:10.1007/978-3-642-22993-0_3 fatcat:wypwkdeib5gvxaibobuobdlhui

A Survey on Operational State Complexity [article]

Yuan Gao and Nelma Moreira and Rogério Reis and Sheng Yu
2015 arXiv   pre-print
Operational state 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.  ... 
arXiv:1509.03254v1 fatcat:oxleg7kkvvezxoqgscdnlghzvu

Most Complex Regular Ideal Languages [article]

Janusz Brzozowski, Sylvie Davies, Bo Yang Victor Liu
2016 arXiv   pre-print
In that sense, these ideals are "most 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.  ... 
arXiv:1511.00157v3 fatcat:5ssf2cwvf5fnhpv3feucvq2sau
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