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Quotient complexity of starfree languages
, 2010
"... The quotient complexity, also known as state complexity, of a regular language is the number of distinct left quotients of the language. The quotient complexity of an operation is the maximal quotient complexity of the language resulting from the operation, as a function of the quotient complexiti ..."
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Cited by 7 (3 self)
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The quotient complexity, also known as state complexity, of a regular language is the number of distinct left quotients of the language. The quotient complexity of an operation is the maximal quotient complexity of the language resulting from the operation, as a function of the quotient complexities of the operands. The class of starfree languages is the smallest class containing the finite languages and closed under boolean operations and concatenation. We prove that the tight bounds on the quotient complexities of union, intersection, difference, symmetric difference, concatenation, and star for starfree languages are the same as those for regular languages, with some small exceptions, whereas the bound for reversal is 2n − 1.
Incomplete Transition Complexity of some Basic Operations
"... Abstract. Y. Gao et al. studied for the first time the transition complexity of Boolean operations on regular languages based on not necessarily complete DFAs. For the intersection and the complementation, tight bounds were presented, but for the union operation the upper and lower bounds differ by ..."
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Abstract. Y. Gao et al. studied for the first time the transition complexity of Boolean operations on regular languages based on not necessarily complete DFAs. For the intersection and the complementation, tight bounds were presented, but for the union operation the upper and lower bounds differ by a factor of two. In this paper we continue this study by giving tight upper bounds for the concatenation, the Kleene star and the reversal operations. We also give a new tight upper bound for the transition complexity of the union, which refutes the conjecture presented by Y. Gao et al..
Departamento de Ciência de Computadores Faculdade de Ciências da Universidade do Porto
, 2011
"... Abstract. The state complexity of a regular language is the number of states of its minimal determinitisc finite automaton. The complexity of a language operation is the complexity of the resulting language seen as a function of the complexities of the operation arguments. In this report we review s ..."
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Abstract. The state complexity of a regular language is the number of states of its minimal determinitisc finite automaton. The complexity of a language operation is the complexity of the resulting language seen as a function of the complexities of the operation arguments. In this report we review some of the results of state complexity of individual operations for regular and some subregular languages. 1 State Complexity and Nondeterministic State Complexity The state complexity of a regular language L, sc(L), is the number of states of its minimal DFA. The nondeterministic state complexity of a regular language L, nsc(L), is the number of states of a minimal NFA that accepts L. Since a DFA is in particular an NFA, for any regular language L one has sc(L) ≤ nsc(L). It is well knownthatanymstateNFAcanbeconverted,viathesubset construction,inanequivalentDFAwith at most 2 m states [114] (we call this conversion determination). Thus, sc(L) ≤ 2 nsc(L). To show that (i) (ii) (iii)
A Review on State Complexity of Individual Operations
"... Abstract. The state complexity of a regular language is the number of states of its minimal determinitisc finite automaton. The complexity of a language operation is the complexity of the resulting language seen as a function of the complexities of the operation arguments. In this report we review s ..."
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Abstract. The state complexity of a regular language is the number of states of its minimal determinitisc finite automaton. The complexity of a language operation is the complexity of the resulting language seen as a function of the complexities of the operation arguments. In this report we review some of the results of state complexity of individual operations for regular and some subregular languages. 1 State Complexity and Nondeterministic State Complexity The state complexity of a regular language L, sc(L), is the number of states of its minimal DFA. The nondeterministic state complexity of a regular language L, nsc(L), is the number of states of a minimal NFA that accepts L. Since a DFA is in particular an NFA, for any regular language L one has sc(L) ≤ nsc(L). It is well known that anymstate NFA can be converted, via the subset construction, in an equivalent DFA with at most 2m states [116] (we call this conversion determination). Thus, sc(L) ≤ 2nsc(L). To show that (i) 0 1 2 · · · m − 2 m − 1