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68
Quotient complexity of regular languages
 J. Autom. Lang. Comb
, 2010
"... The past research on the state complexity of operations on regular languages is examined, and a new approach based on an old method (derivatives of regular expressions) is presented. Since state complexity is a property of a language, it is appropriate to define it in formallanguage terms as the nu ..."
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Cited by 42 (28 self)
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The past research on the state complexity of operations on regular languages is examined, and a new approach based on an old method (derivatives of regular expressions) is presented. Since state complexity is a property of a language, it is appropriate to define it in formallanguage terms as the number of distinct quotients of the language, and to call it “quotient complexity”. The problem of finding the quotient complexity of a language f(K,L) is considered, where K and L are regular languages and f is a regular operation, for example, union or concatenation. Since quotients can be represented by derivatives, one can find a formula for the typical quotient of f(K,L) in terms of the quotients of K and L. To obtain an upper bound on the number of quotients of f(K,L) all one has to do is count how many such quotients are possible, and this makes automaton constructions unnecessary. The advantages of this point of view are illustrated by many examples. Moreover, new general observations are presented to help in the estimation of the upper bounds on quotient complexity of regular operations. 1
M.: State complexity of basic operations on nondeterministic finite automata
 In: In Implementation and Application of Automata (CIAA’02), LNCS 2608
, 2001
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State complexity of basic operations on suffixfree regular languages
, 2007
"... We investigate the state complexity of basic operations for suffixfree regular languages. The state complexity of an operation for regular languages is the number of states that are necessary and sufficient in the worstcase for the minimal deterministic finitestate automaton that accepts the lan ..."
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Cited by 25 (4 self)
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We investigate the state complexity of basic operations for suffixfree regular languages. The state complexity of an operation for regular languages is the number of states that are necessary and sufficient in the worstcase for the minimal deterministic finitestate automaton that accepts the language obtained from the operation. We establish the precise state complexity of catenation, Kleene star, reversal and the Boolean operations for suffixfree regular languages.
Y.: Syntactic complexity of ideal and closed languages
, 2010
"... Abstract. The state complexity of a regular language is the number of states in the minimal deterministic automaton accepting the language. The syntactic complexity of a regular language is the cardinality of its syntactic semigroup. The syntactic complexity of a subclass of regular languages is the ..."
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Cited by 21 (16 self)
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Abstract. The state complexity of a regular language is the number of states in the minimal deterministic automaton accepting the language. The syntactic complexity of a regular language is the cardinality of its syntactic semigroup. The syntactic complexity of a subclass of regular languages is the worstcase syntactic complexity taken as a function of the state complexity n of languages in that class. We prove that nn−1 is a tight upper bound on the complexity of right ideals and prefixclosed languages, and that there exist left ideals and suffixclosed languages of syntactic complexity nn−1+n−1, and twosided ideals and factorclosed languages of syntactic complexity nn−2 + (n − 2)2n−2 + 1.
Nondeterministic descriptional complexity of regular languages
 Internat. J. Found. Comput. Sci
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Quotient complexity of closed languages
 Computer Science  Theory and Applications, 5th International Computer Science Symposium in Russia, CSR 2010
"... Abstract. A language L is prefixclosed if, whenever a word w is in L, then every prefix of w is also in L. We define suffix, factor, and subwordclosed languages in an analogous way, where by subword we mean subsequence. We study the quotient complexity (usually called state complexity) of oper ..."
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Cited by 14 (8 self)
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Abstract. A language L is prefixclosed if, whenever a word w is in L, then every prefix of w is also in L. We define suffix, factor, and subwordclosed languages in an analogous way, where by subword we mean subsequence. We study the quotient complexity (usually called state complexity) of operations on prefix, suffix, factor, and subwordclosed languages. We find tight upper bounds on the complexity of the subwordclosure of arbitrary languages, and on the complexity of boolean operations, concatenation, star, and reversal in each of the four classes of closed languages. We show that repeated application of positive closure and complement to a closed language results in at most four distinct languages, while Kleene closure and complement gives at most eight.
Quotient complexity of bifix, factor, and subwordfree languages. http://arxiv.org/abs/1006.4843v3
, 2011
"... A language L is prefixfree if, whenever words u and v are in L and u is a prefix of v, then u = v. Suffix, factor, and subwordfree languages are defined similarly, where “subword ” means “subsequence”. A language is bifixfree if it is both prefix and suffixfree. We study the quotient complex ..."
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Cited by 13 (9 self)
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A language L is prefixfree if, whenever words u and v are in L and u is a prefix of v, then u = v. Suffix, factor, and subwordfree languages are defined similarly, where “subword ” means “subsequence”. A language is bifixfree if it is both prefix and suffixfree. We study the quotient complexity, more commonly known as state complexity, of operations in the classes of bifix, factor, and subwordfree regular languages. We find tight upper bounds on the quotient complexity of intersection, union, difference, symmetric difference, concatenation, star, and reversal in these three classes of languages. 1
State complexity and the monoid of transformations of a finite set
, 2003
"... In this paper we consider the state complexity of an operation on formal languages, root(L). This naturally entails the study of the monoid of transformations of a finite set. We obtain lower bounds on the state complexity of root(L) and the size of the largest submonoid generated by two elements. 1 ..."
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Cited by 12 (0 self)
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In this paper we consider the state complexity of an operation on formal languages, root(L). This naturally entails the study of the monoid of transformations of a finite set. We obtain lower bounds on the state complexity of root(L) and the size of the largest submonoid generated by two elements. 1
Syntactic Complexity of Prefix, Suffix, and BifixFree Regular Languages
"... Abstract. The syntactic complexity of a regular language is the cardinality of its syntactic semigroup. 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 lan ..."
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Cited by 12 (10 self)
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Abstract. The syntactic complexity of a regular language is the cardinality of its syntactic semigroup. 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, and bifixfree regular languages. We prove that nn−2 is a tight upper bound for prefixfree regular languages. We present properties of the syntactic semigroups of suffix and bifixfree regular languages, and conjecture tight upper bounds on their size.
Descriptional Complexity of Machines with Limited Resources
 J. UNIVERSAL COMPUTER SCI
, 2002
"... Over the last 30 years or so many results have appeared on the descriptional complexity of machines with limited resources. Since these results have appeared in a variety of different contexts, o rgo4 here is to pro vide a survey o these results. Particular emphasis is put o limiting reso rces (e.g. ..."
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Cited by 12 (3 self)
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Over the last 30 years or so many results have appeared on the descriptional complexity of machines with limited resources. Since these results have appeared in a variety of different contexts, o rgo4 here is to pro vide a survey o these results. Particular emphasis is put o limiting reso rces (e.g., no ndeterminism, ambiguity,lo o ahead, etc.) fo vario s types o finite state machines, pushdo wn auto mata, parsers and cellular auto mata ando n the e#ect it haso n their descriptio nal co mplexity. We also address the questio no f how descriptional complexity might help in the future to solve practical issues, such as software reliability.