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

Janusz Brzozowski
2016 Lecture Notes in Computer Science  
I study the 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.  ... 
doi:10.1007/978-3-319-41114-9_5 fatcat:2oxodptgb5bqxn5znttxl43vwy

State Complexity of Pattern Matching in Regular Languages [article]

Janusz A. Brzozowski, Sylvie Davies, Abhishek Madan
2018 arXiv   pre-print
The 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.  ... 
arXiv:1806.04645v2 fatcat:2n5znnhpqzgg5li2pajdqy6sc4

Unrestricted State Complexity of Binary Operations on Regular and Ideal Languages [article]

Janusz Brzozowski, Corwin Sinnamon
2017 arXiv   pre-print
We study the 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.  ... 
arXiv:1609.04439v3 fatcat:6lkl7d2k2jczvn64nf2ba25bnm

On the State Complexity of the Shuffle of Regular Languages [chapter]

Janusz Brzozowski, Galina Jirásková, Bo Liu, Aayush Rajasekaran, Marek Szykuła
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 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.  ... 
doi:10.1007/978-3-319-41114-9_6 fatcat:brg4mg3r5zgvtofd2lecc3vw2i

On the state complexity of reversals of regular languages

Arto Salomaa, Derick Wood, Sheng Yu
2004 Theoretical Computer Science  
In the worst case the 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] .  ... 
doi:10.1016/j.tcs.2004.02.032 fatcat:swbz3zzy5jcthm4rnxvgt4cwtq

State complexity of the concatenation of regular tree languages

Xiaoxue Piao, Kai Salomaa
2012 Theoretical Computer Science  
We consider the 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.  ... 
doi:10.1016/j.tcs.2011.12.048 fatcat:sn4srx24xvdnrbkhxih6i4sdfy

On the state complexity of reversals of regular languages

A SALOMAA
2004 Theoretical Computer Science  
In the worst case the 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] .  ... 
doi:10.1016/s0304-3975(04)00131-8 fatcat:x4o5f2czbveotij22gtxpn26vu

State complexity of some operations on binary regular languages

Galina Jirásková
2005 Theoretical Computer Science  
We investigate the 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.  ... 
doi:10.1016/j.tcs.2004.04.011 fatcat:tu6bumk2ercixn2olnzsu2ljau

On the state complexity of closures and interiors of regular languages with subwords and superwords

P. Karandikar, M. Niewerth, Ph. Schnoebelen
2016 Theoretical Computer Science  
We also consider the computational 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.  ... 
doi:10.1016/j.tcs.2015.09.028 fatcat:llxtak6i5fgzlp6ybu6zr4mjeq

On the State Complexity of the Reverse of R- and J-trivial Regular Languages [article]

Galina Jirásková, Tomáš Masopust
2013 arXiv   pre-print
The tight upper bound on the 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.  ... 
arXiv:1304.0733v2 fatcat:itkv4isu5nd2bprgkhjhemky2e

State Complexity of Kleene-Star Operations on Regular Tree Languages

Yo-Sub Han, Sang-Ki Ko, Xiaoxue Piao, Kai Salomaa
2015 Acta Cybernetica  
The 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.  ... 
doi:10.14232/actacyb.22.2.2015.11 fatcat:lemjqtbmr5devkuisojhb34t4e

State Complexity of Regular Tree Languages for Tree Pattern Matching [chapter]

Sang-Ki Ko, Ha-Rim Lee, Yo-Sub Han
2014 Lecture Notes in Computer Science  
We study the 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] .  ... 
doi:10.1007/978-3-319-09704-6_22 fatcat:j24fr5loanfptjl62cgokfs7i4

The state complexities of some basic operations on regular languages

Sheng Yu, Qingyu Zhuang, Kai Salomaa
1994 Theoretical Computer Science  
We consider the 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  ... 
doi:10.1016/0304-3975(92)00011-f fatcat:c4gkvsq4wrbpjigd76ouxj6kwy

State complexity of basic operations on suffix-free regular languages

Yo-Sub Han, Kai Salomaa
2009 Theoretical Computer Science  
We investigate the 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.  ... 
doi:10.1016/j.tcs.2008.12.054 fatcat:hoer4hpsivdanl2ul5lkc7zzgm

State complexity of union and intersection of star on regular languages

Yuan Gao, Lila Kari, Sheng Yu
2012 Theoretical Computer Science  
We study the 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.  ... 
doi:10.1016/j.tcs.2011.12.028 fatcat:5gebkukzkzb35irltgpkgy2oym
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