Unary language operations, state complexity and jacobsthal's function

International Journal of Foundations of Computer Science

Volumn 13, Issue 1, 2002, Pages 145-159

  Pighizzini, Giovanni ^a   Shallit, Jeffrey ^b  

^a UNIVERSITY OF MILAN   (Italy)

^b UNIVERSITY OF WATERLOO   (Canada)

Author keywords

Finite automata; formal languages; number theory; state complexity; unary languages

Indexed keywords

EID: 11844282318     PISSN: 01290541     EISSN: None     Source Type: Journal    
DOI: 10.1142/S012905410200100X     Document Type: Conference Paper

References (19)

1. S. D. Adhikari and R. Balasubramanian. On a question regarding visibility of lattice points. Mathematika, 43:155-158, 1996.
2. E. Bach and J. Shallit. Algorithmic Number Theory. MIT Press, 1996.
3. A. Brauer. On a problem of partitions. Amer. J. Math., 64:299-312, 1942.
4. M. Chrobak. Finite automata and unary languages. Theoretical Computer Science, 47:149-158, 1986.
5. Yu. L. Ershov. On a conjecture of V. A. Uspenskii. Algebra i Logika l:(4):45-48, 1962. (In Russian).
6. J. E. Hopcroft and J. D. Ullman. Introduction to Automata Theory, Languages, and Computation. Addison-Wesley, 1979.
7. H. Iwaniec. On the problem of Jacobsthal. Dem. Math., 11:225-231, 1978.
8. E. Jacobsthal. Uber Sequenzen ganzer Zahlen, von denen keine zu n teilerfremd ist. I-III. Norske Vid. Selsk. Forh. Trondheim, 33:117-139, 1960.
9. H.-J. Kanold. Uber eine zahlentheoretische Funktion von Jacobsthal. Math. Annalen, 170:314-326, 1967.
10. Yu. I. Lyubich. Estimates for optimal determinization of nondeterministic autonomous automata. Sibirskii Matemat. Journal, 5:(2):337-355, 1964. (In Russian).
11. Yu. I. Lyubich. Estimates of the number of states that arise in the determinization of a nondeterministc autonomous automaton. Doklady Akad. Nauk SSSR, 155:(1):41-43, 1964. In Russian. English translation in Soviet Mathematics 5:345-348, 1964.
12. R. Mandl. Precise bounds associated with the subset construction on various classes of nondeterministic finite automata. In Proc. 7th Princeton Conference on Information and System Science, 263-267, 1973.
13. A. R. Meyer and M. J. Fischer. Economy of description by automata, grammars, and formal systems. In Conference Record 1971 Twelfth Annual Symposium on Switching and Automata Theory, IEEE Computer Society, pp. 188-191, 1971.
14. F. R. Moore. On the bounds for state-set size in the proofs of equivalence between deterministic, nondeterministic, and two-way finite automata. IEEE Trans. Computers, 20:1211-1214, 1971.
15. C. Nicaud. Average state complexity of operations on unary automata. In M. Kutylowski, L. Pacholski, and T. Wierzbicki, editors, Proc. 24th Symposium, Mathematical Foundations of Computer Science 1999, Vol. 1672 of Lecture Notes in Computer Science, pp. 231-240. Springer-Verlag, 1999.
16. G. Robin. Estimation de la fonction de Tchebychef 6 sur le fc-ieme nombre premier et grandes valeurs de la fonction UJ(JI) nombre de diviseurs premiers de n. Acta Arith., 42:367-389, 1983.
17. S. Yu. State complexity of regular languages. In International Workshop on Descriptional Complexity of Automata, Grammars and Related Structures, Preproceedings, pp. 77-88. Department of Computer Science, Otto-von-Guericke University of Magdeburg, July 1999.
18. S. Yu and Q. Zhuang. On the state complexity of intersection of regular languages. SIGACT News, 22(3):52-54, Summer 1991.
19. S. Yu, Q. Zhuang, and K. Salomaa. The state complexity of some basic operations on regular languages. Theoret. Comput. Sci., 125:315-328, 1994.