559 research outputs found
State complexity of catenation combined with a boolean operation: a unified approach
In this paper we study the state complexity of catenation combined with
symmetric difference. First, an upper bound is computed using some combinatoric
tools. Then, this bound is shown to be tight by giving a witness for it.
Moreover, we relate this work with the study of state complexity for two other
combinations: catenation with union and catenation with intersection. And we
extract a unified approach which allows to obtain the state complexity of any
combination involving catenation and a binary boolean operation
State Complexity of Combined Operations on Finite Languages
State complexity is a descriptive complexity measure for regular languages. It is a fundamental topic in automata and formal language theory. The state complexity of a regular language is the number of states in the minimal complete deterministic finite automaton accepting the language. During the last few decades, many publications have focused and studied the state complexity of many individual as well as combined operations on regular languages. Also, the state complexity of some basic operations on finite languages has been studied. But until now there has been no study on the state complexity of combined operations on finite languages.
In this thesis, we will first study the state complexity of the combined operation, star of union, on finite languages and give an exact bound. Then we will investigate the state complexity of star of catenation and show its approximation with a good ratio bound and finally, we will prove an upper bound for star of intersection
State Complexity of Catenation Combined with Star and Reversal
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.Comment: In Proceedings DCFS 2010, arXiv:1008.127
Universal Witnesses for State Complexity of Basic Operations Combined with Reversal
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 witnesses and their variants.Comment: 18 pages, 8 figures. LNCS forma
Advanced Topics on State Complexity of Combined Operations
State complexity is a fundamental topic in formal languages and automata theory. The study of state complexity is also strongly motivated by applications of finite automata in software engineering, programming languages, natural language and speech processing and other practical areas. Since many of these applications use automata of large sizes, it is important to know the number of states of the automata. In this thesis, we firstly discuss the state complexities of individual operations on regular languages, including union, intersection, star, catenation, reversal and so on. The state complexity of an operation on unary languages is usually different from that of the same operation on languages over a larger alphabet. Both kinds of state complexities are reviewed in the thesis. Secondly, we study the exact state complexities of twelve combined operations on regular languages. The state complexities of most of these combined operations are not equal to the compositions of the state complexities of the individual operations which make up these combined operations. We also explore the reason for this difference. Finally, we introduce the concept of estimation and approximation of state complexity. We show close estimates and approximations of the state complexities of six combined operations on regular languages which are good enough to use in practice
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