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Unrestricted State Complexity of Binary Operations on Regular Languages
[chapter]

2016
*
Lecture Notes in Computer Science
*

I study the

doi:10.1007/978-3-319-41114-9_5
fatcat:2oxodptgb5bqxn5znttxl43vwy
*state**complexity**of*binary operations on*regular**languages*over different alphabets. ... It is well known that if L'_m and L_n are*languages*restricted to be over the same alphabet, with m and n quotients, respectively, the*state**complexity**of*any binary boolean operation on L'_m and L_n is ... Let L ′ m ⊆ Σ ′ * and L n ⊆ Σ * be*regular**languages**of**complexities*m and n, respectively. ...##
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State Complexity of Pattern Matching in Regular Languages
[article]

2018
*
arXiv
*
pre-print

The

arXiv:1806.04645v2
fatcat:2n5znnhpqzgg5li2pajdqy6sc4
*state**complexity*κ(L)*of*a*regular**language*L is the number*of**states*in the minimal deterministic finite automaton recognizing L. ... More generally, we may have a set P*of*patterns and a set T*of*texts, where P and T are*regular**languages*. ... The*state**complexity**of*a*regular**language*L, denoted by κ(L), is the number*of**states*in the minimal DFA accepting L. ...##
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Unrestricted State Complexity of Binary Operations on Regular and Ideal Languages
[article]

2017
*
arXiv
*
pre-print

We study the

arXiv:1609.04439v3
fatcat:6lkl7d2k2jczvn64nf2ba25bnm
*state**complexity**of*binary operations on*regular**languages*over different alphabets. ... The*state**complexities**of*boolean operations on all three types*of*ideals are the same as those*of*arbitrary*regular**languages*, whereas that is not the case if the alphabets*of*the arguments are the same ... The*state**complexity*[24]*of*a*regular**language*L is the number*of**states*in a complete minimal DFA with alphabet Σ L which recognizes the*language*. ...##
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On the State Complexity of the Shuffle of Regular Languages
[chapter]

2016
*
Lecture Notes in Computer Science
*

We prove that f(m,n)=2^mn-1 + 2^(m-1)(n-1)(2^m-1-1)(2^n-1-1) is an upper bound on the

doi:10.1007/978-3-319-41114-9_6
fatcat:brg4mg3r5zgvtofd2lecc3vw2i
*state**complexity**of*the shuffle*of*two*regular**languages*having*state**complexities*m and n, respectively. ... We investigate the shuffle operation on*regular**languages*represented by complete deterministic finite automata. ... on two*regular**languages**of**state**complexities*m and n, respectively, and found an upper bound for it. ...##
###
On the state complexity of reversals of regular languages

2004
*
Theoretical Computer Science
*

In the worst case the

doi:10.1016/j.tcs.2004.02.032
fatcat:swbz3zzy5jcthm4rnxvgt4cwtq
*state**complexity**of*the reversal is 2 n for an n-*state**language*. ... We compare the number*of**states*between minimal deterministic ÿnite automata accepting a*regular**language*and its reversal (mirror image). ... The*state**complexity**of*a*regular**language*is the*state**complexity**of*the minimal DFA for the*language*.*State**complexities**of*many basic operations have been studied in [8] . ...##
###
State complexity of the concatenation of regular tree languages

2012
*
Theoretical Computer Science
*

We consider the

doi:10.1016/j.tcs.2011.12.048
fatcat:sn4srx24xvdnrbkhxih6i4sdfy
*state**complexity**of*basic concatenation operations for*regular*tree*languages*. ... The bound for sequential concatenation*of*tree*languages*differs by an order*of*magnitude from the corresponding bound for*regular*string*languages*. ... This bound is*of*a different order*of*magnitude than the known*state**complexity**of*concatenation*of**regular*string*languages*. ...##
###
On the state complexity of reversals of regular languages

2004
*
Theoretical Computer Science
*

In the worst case the

doi:10.1016/s0304-3975(04)00131-8
fatcat:x4o5f2czbveotij22gtxpn26vu
*state**complexity**of*the reversal is 2 n for an n-*state**language*. ... We compare the number*of**states*between minimal deterministic ÿnite automata accepting a*regular**language*and its reversal (mirror image). ... The*state**complexity**of*a*regular**language*is the*state**complexity**of*the minimal DFA for the*language*.*State**complexities**of*many basic operations have been studied in [8] . ...##
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State complexity of some operations on binary regular languages

2005
*
Theoretical Computer Science
*

We investigate the

doi:10.1016/j.tcs.2004.04.011
fatcat:tu6bumk2ercixn2olnzsu2ljau
*state**complexity**of*some operations on binary*regular**languages*. ... We prove that the upper bounds on the*state**complexity**of*these operations, which were known to be tight for larger alphabets, are tight also for binary alphabets. ... Acknowledgements I would like to thank Jožko Jirásek for his help with the computational verification*of*some conjectures. ...##
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On the state complexity of closures and interiors of regular languages with subwords and superwords

2016
*
Theoretical Computer Science
*

We also consider the computational

doi:10.1016/j.tcs.2015.09.028
fatcat:llxtak6i5fgzlp6ybu6zr4mjeq
*complexity**of*decision problems for closures*of**regular**languages*. ... The downward and upward closures*of*a*regular**language*L are obtained by collecting all the subwords and superwords*of*its elements, respectively. ... Schmitz and the anonymous reviewers for their many comments and suggestions that helped improve the final version*of*this article. ...##
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On the State Complexity of the Reverse of R- and J-trivial Regular Languages
[article]

2013
*
arXiv
*
pre-print

The tight upper bound on the

arXiv:1304.0733v2
fatcat:itkv4isu5nd2bprgkhjhemky2e
*state**complexity**of*the reverse*of*R-trivial and J-trivial*regular**languages**of*the*state**complexity*n is 2^n-1. ... We provide a characterization*of*tight bounds for R-trivial*regular**languages*depending on the*state**complexity**of*the*language*and the size*of*its alphabet. ... The authors gratefully acknowledge very useful suggestions and comments*of*anonymous referees on the previous version*of*this work. ...##
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State Complexity of Kleene-Star Operations on Regular Tree Languages

2015
*
Acta Cybernetica
*

The

doi:10.14232/actacyb.22.2.2015.11
fatcat:lemjqtbmr5devkuisojhb34t4e
*state**complexity**of*top-down star is similar as in the string case. We consider also the*state**complexity**of*the star*of*the concatenation*of*a*regular*tree*language*with the set*of*all trees. ... We establish that the worst-case*state**complexity**of*bottom-up star is (n + 3 2 ) · 2 n−1 . The bound differs by an order*of*magnitude from the corresponding result for string*languages*. ... Next we give a tight*state**complexity*bound for top-down star*of**regular*tree*languages*. ...##
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State Complexity of Regular Tree Languages for Tree Pattern Matching
[chapter]

2014
*
Lecture Notes in Computer Science
*

We study the

doi:10.1007/978-3-319-09704-6_22
fatcat:j24fr5loanfptjl62cgokfs7i4
*state**complexity**of**regular*tree*languages*for tree matching problem. ... We consider the case when we are given a set*of*pattern trees as a*regular*tree*language*and investigate the*state**complexity*. ... Two*of*the authors studied the*state**complexity**of*subtree-free*regular*tree*languages*, which are a proper subclass*of**regular*tree*languages*[3] . ...##
###
The state complexities of some basic operations on regular languages

1994
*
Theoretical Computer Science
*

We consider the

doi:10.1016/0304-3975(92)00011-f
fatcat:c4gkvsq4wrbpjigd76ouxj6kwy
*state**complexities**of*some basic operations on*regular**languages*. ... Salomaa, The*state**complexities**of*some basic operations on*regular**languages*, Theoretical Computer Science 125 (1994) 315-328. ... Now it is clear that L(C)=L(A)C*. 0*State**complexity**of*star operation on*regular**languages*In [S] , an example is given to show that any DFA accepting the star*of*an n-*state*DFA*language*needs at least ...##
###
State complexity of basic operations on suffix-free regular languages

2009
*
Theoretical Computer Science
*

We investigate the

doi:10.1016/j.tcs.2008.12.054
fatcat:hoer4hpsivdanl2ul5lkc7zzgm
*state**complexity**of*basic operations for suffix-free*regular**languages*. ... The*state**complexity**of*an operation for*regular**languages*is the number*of**states*that are necessary and sufficient in the worst-case for the minimal deterministic finite-*state*automaton that accepts ... Han was supported by the IT R&D program*of*MKE/IITA 2008-S-024-01 and Salomaa was supported by the Natural Sciences and Engineering Research Council*of*Canada Grant OGP0147224. ...##
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State complexity of union and intersection of star on regular languages

2012
*
Theoretical Computer Science
*

We study the

doi:10.1016/j.tcs.2011.12.028
fatcat:5gebkukzkzb35irltgpkgy2oym
*state**complexities**of*We obtain the exact bounds for these combined operations and show that the bounds are different from the mathematical compositions*of*the*state**complexities**of*their ... In this paper, we continue our study on*state**complexity**of*combined operations. ... The*state**complexity**of*an operation on*regular**languages*is the*state**complexity**of*the resulting*languages*from the operation as a function*of*the*state**complexity**of*the operand*languages*. ...
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