The state complexities of some basic operations on regular languages
Theoretical Computer Science
An introduction to the analysis of algorithms
An introduction to the analysis of algorithms
Transcendence of formal power series with rational coefficients
Theoretical Computer Science
Automata, Languages, and Machines
Automata, Languages, and Machines
Introduction To Automata Theory, Languages, And Computation
Introduction To Automata Theory, Languages, And Computation
State Complexity and Jacobsthal's Function
CIAA '00 Revised Papers from the 5th International Conference on Implementation and Application of Automata
Unary Language Concatenation and Its State Complexity
CIAA '00 Revised Papers from the 5th International Conference on Implementation and Application of Automata
Nondeterministic Finite Automata--Recent Results on the Descriptional and Computational Complexity
CIAA '08 Proceedings of the 13th international conference on Implementation and Applications of Automata
State Complexity of Combined Operations for Prefix-Free Regular Languages
LATA '09 Proceedings of the 3rd International Conference on Language and Automata Theory and Applications
Average complexity of Moore's and Hopcroft's algorithms
Theoretical Computer Science
On the state complexity of combined operations
CIAA'06 Proceedings of the 11th international conference on Implementation and Application of Automata
The State Complexity of Two Combined Operations: Star of Catenation and Star of Reversal
Fundamenta Informaticae
State Complexity: Recent Results and Open Problems
Fundamenta Informaticae - Contagious Creativity - In Honor of the 80th Birthday of Professor Solomon Marcus
State complexity of basic operations on suffix-free regular languages
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
State complexity of combined operations for suffix-free regular languages
Theoretical Computer Science
Hi-index | 0.00 |
Define the complexity of a regular language as the number of states of its minimal automaton. Let A (respectively A') be an n-state (resp. n'-state) deterministic and connected uneiry automaton. Our main results can be summarized ais follows: 1. The probability that A is minimal tends toweird 1/2 when n tends toward infinity, 2. The average complexity of L(A) is equivalent to n, 3. The average complexity of L(A) ∩ L(A') is equivalent to 3ç(3)/2π2nn', where ç is the Riemann "zeta"-function. 4. The average complexity of L(A)* is bounded by a constrant, 5. If n ≤ n' ≤ P(n), for some polynomial P, the average complexity of L(A)L(A') is bounded by a constant (depending on P). Remark that results 3, 4 and 5 differ perceptibly from the corresponding worst case complexities, which are nn' for intersection, (n - 1)2 + 1 for star and nn' for concatenation product.