State Complexity of Four Combined Operations Composed of Union, Intersection, Star and Reversal

2011 ◽  
pp. 158-171 ◽  
Author(s):  
Yuan Gao ◽  
Sheng Yu
Keyword(s):  
State Complexity ◽  
Combined Operations

STATE COMPLEXITY AND APPROXIMATION

2012 ◽  
Vol 23 (05) ◽  
pp. 1085-1098 ◽  
Author(s):  
YUAN GAO ◽  
SHENG YU
Keyword(s):  
The State ◽  
General Algorithm ◽  
Future Research ◽  
State Complexity ◽  
Combined Operations ◽  
Essential Questions

We discuss a number of essential questions concerning the state complexity research. The questions include why many basic problems were not studied earlier, whether there is a general algorithm for state complexity of combined operations, and whether there is a new and effective approach in this area of research. The concept of state complexity approximation is also discussed. We show that state complexity approximation can be used to obtain good results when the exact state complexities are difficult to find and when the exact state complexities are too complex to comprehend. We also list a number of questions for future research in this area.

ON THE STATE COMPLEXITY OF COMBINED OPERATIONS AND THEIR ESTIMATION

2007 ◽  
Vol 18 (04) ◽  
pp. 683-698 ◽  
Author(s):  
KAI SALOMAA ◽  
SHENG YU
Keyword(s):  
Large Class ◽  
The State ◽  
Estimation Methods ◽  
State Complexity ◽  
Combined Operations ◽  
Combined Operation ◽  
Nondeterministic State ◽  
General Estimation

We consider the state complexity of several combined operations. Those results show that the state complexity of a combined operation is in general very different from the composition of the state complexities of the participating individual operations. We also consider general estimation methods for the state complexity of combined operations. In particular, estimation through nondeterministic state complexity is studied. It is shown that the method is very promising for a large class of combined operations.

STATE COMPLEXITY OF TWO COMBINED OPERATIONS: CATENATION-STAR AND CATENATION-REVERSAL

2012 ◽  
Vol 23 (01) ◽  
pp. 51-66 ◽  
Author(s):  
BO CUI ◽  
YUAN GAO ◽  
LILA KARI ◽  
SHENG YU
Keyword(s):  
Research Work ◽  
The State ◽  
State Complexity ◽  
Combined Operations

This paper is a continuation of our research work on state complexity of combined operations. Motivated by applications, we study the state complexities of two particular combined operations: catenation combined with star and catenation combined with reversal. We show that the state complexities of both of these combined operations are considerably less than the compositions of the state complexities of their individual participating operations.

scholarly journals State complexity of combined operations

2007 ◽  
Vol 383 (2-3) ◽  
pp. 140-152 ◽  
Author(s):  
Arto Salomaa ◽  
Kai Salomaa ◽  
Sheng Yu
Keyword(s):  
State Complexity ◽  
Combined Operations

STATE COMPLEXITY OF TWO COMBINED OPERATIONS: CATENATION-UNION AND CATENATION-INTERSECTION

2011 ◽  
Vol 22 (08) ◽  
pp. 1797-1812 ◽  
Author(s):  
BO CUI ◽  
YUAN GAO ◽  
LILA KARI ◽  
SHENG YU
Keyword(s):  
The State ◽  
State Complexity ◽  
Combined Operations ◽  
Combined Operation

In this paper, we study the state complexities of two particular combinations of operations: catenation combined with union and catenation combined with intersection. We show that the state complexity of the former combined operation is considerably less than the mathematical composition of the state complexities of catenation and union, while the state complexity of the latter one is equal to the mathematical composition of the state complexities of catenation and intersection.

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