Guangwu Liu - Academia.edu (original) (raw)

Papers by Guangwu Liu

Triangle, 2018

This paper is a summary of my seminars given in the Research Group on Mathematical Linguistics in... more This paper is a summary of my seminars given in the Research Group on Mathematical Linguistics in the year 2005. It is a short survey on automata theory, including nite state automata and tree automata. The transformations (transductions) induced by nite state automata and tree automata are given.

We study the state complexity of boolean operations, concatenation, and star, with one or two of ... more We study the state complexity of boolean operations, concatenation, and star, with one or two of the argument languages reversed. We derive tight upper bounds for the symmetric differences and differences of such languages. We prove that the previously discovered bounds for union, intersection, concatenation and star of such languages can all be met by the recently introduced universal witness and its variants.

In the last decade, many new results in the area of state complexity have been obtained. Some are... more In the last decade, many new results in the area of state complexity have been obtained. Some are about Boolean operations, e.g. intersection, union and catenation and most of them focused on the cases of these operations on two languages. But in the practical applications, these operations are often required to be performed multiple times on three or more languages. The state complexity of these operations on k languages may not necessarily equal to the k-1 times direct combination of their state complexities on two languages. Thus, it is important to study the state complexities of multiple Boolean operations. Several results about the state complexities of intersection and union on k regular languages are given and proved here. The state complexities are also obtained in the cases of the catenations of three and four languages.

Theoretical Computer Science, 2009

It appears that the state complexity of each combined operation has its own special features. Thu... more It appears that the state complexity of each combined operation has its own special features. Thus, it is important and practical to obtain good estimates for some commonly used general cases. In this paper, we consider the state complexity of combined Boolean operations and give an exact bound for all of them in the case when the alphabet is not fixed. Moreover, we show that for any fixed alphabet, this bound can be reached in infinitely many cases. We also consider the state complexity of multiple catenations. The state complexities are obtained in the cases of the catenations of three and four languages. An estimate for the catenation of an arbitrary number of languages is given, which is very close to the state complexities in the three and four languages cases.

Information and Computation, 2008

We study the state complexity of combined operations on regular languages. Each of the combined o... more We study the state complexity of combined operations on regular languages. Each of the combined operations is a basic operation combined with reversal. We show that their state complexities are all very different from the compositions of state complexities of individual operations.

Fuzzy Sets and Systems, 2007

ABSTRACT In this paper, we map an arbitrary algebra to a completely distributive lattice and defi... more ABSTRACT In this paper, we map an arbitrary algebra to a completely distributive lattice and define algebras of fuzzy sets. When the algebra is a term algebra, we obtain fuzzy tree languages. After defining fuzzy equational sets, fuzzy rational sets and fuzzy recognizable tree languages, we derive a “Kleene theorem” for fuzzy tree languages.

Triangle, 2018

This paper is a summary of my seminars given in the Research Group on Mathematical Linguistics in... more This paper is a summary of my seminars given in the Research Group on Mathematical Linguistics in the year 2005. It is a short survey on automata theory, including nite state automata and tree automata. The transformations (transductions) induced by nite state automata and tree automata are given.

We study the state complexity of boolean operations, concatenation, and star, with one or two of ... more We study the state complexity of boolean operations, concatenation, and star, with one or two of the argument languages reversed. We derive tight upper bounds for the symmetric differences and differences of such languages. We prove that the previously discovered bounds for union, intersection, concatenation and star of such languages can all be met by the recently introduced universal witness and its variants.

In the last decade, many new results in the area of state complexity have been obtained. Some are... more In the last decade, many new results in the area of state complexity have been obtained. Some are about Boolean operations, e.g. intersection, union and catenation and most of them focused on the cases of these operations on two languages. But in the practical applications, these operations are often required to be performed multiple times on three or more languages. The state complexity of these operations on k languages may not necessarily equal to the k-1 times direct combination of their state complexities on two languages. Thus, it is important to study the state complexities of multiple Boolean operations. Several results about the state complexities of intersection and union on k regular languages are given and proved here. The state complexities are also obtained in the cases of the catenations of three and four languages.

Theoretical Computer Science, 2009

It appears that the state complexity of each combined operation has its own special features. Thu... more It appears that the state complexity of each combined operation has its own special features. Thus, it is important and practical to obtain good estimates for some commonly used general cases. In this paper, we consider the state complexity of combined Boolean operations and give an exact bound for all of them in the case when the alphabet is not fixed. Moreover, we show that for any fixed alphabet, this bound can be reached in infinitely many cases. We also consider the state complexity of multiple catenations. The state complexities are obtained in the cases of the catenations of three and four languages. An estimate for the catenation of an arbitrary number of languages is given, which is very close to the state complexities in the three and four languages cases.

Information and Computation, 2008

We study the state complexity of combined operations on regular languages. Each of the combined o... more We study the state complexity of combined operations on regular languages. Each of the combined operations is a basic operation combined with reversal. We show that their state complexities are all very different from the compositions of state complexities of individual operations.

Fuzzy Sets and Systems, 2007

ABSTRACT In this paper, we map an arbitrary algebra to a completely distributive lattice and defi... more ABSTRACT In this paper, we map an arbitrary algebra to a completely distributive lattice and define algebras of fuzzy sets. When the algebra is a term algebra, we obtain fuzzy tree languages. After defining fuzzy equational sets, fuzzy rational sets and fuzzy recognizable tree languages, we derive a “Kleene theorem” for fuzzy tree languages.