Solving parallel equations over $\omega$-languages
Prikladnaâ diskretnaâ matematika, no. 2 (2010), pp. 117-123.

Voir la notice de l'article provenant de la source Math-Net.Ru

The paper is devoted to the problem of solving equations over $\omega$-languages. Similar to formal languages, a solvable equation over $\omega$-languages has the largest solution and the formula of the largest solution is similar to that for formal languages.
Mots-clés : automata equations
Keywords: parallel composition of $\omega$-languages, equations over $\omega$-languages, Büchi automata.
@article{PDM_2010_2_a11,
     author = {V. G. Bushkov and N. V. Yevtushenko},
     title = {Solving parallel equations over $\omega$-languages},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {117--123},
     publisher = {mathdoc},
     number = {2},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2010_2_a11/}
}
TY  - JOUR
AU  - V. G. Bushkov
AU  - N. V. Yevtushenko
TI  - Solving parallel equations over $\omega$-languages
JO  - Prikladnaâ diskretnaâ matematika
PY  - 2010
SP  - 117
EP  - 123
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PDM_2010_2_a11/
LA  - ru
ID  - PDM_2010_2_a11
ER  - 
%0 Journal Article
%A V. G. Bushkov
%A N. V. Yevtushenko
%T Solving parallel equations over $\omega$-languages
%J Prikladnaâ diskretnaâ matematika
%D 2010
%P 117-123
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PDM_2010_2_a11/
%G ru
%F PDM_2010_2_a11
V. G. Bushkov; N. V. Yevtushenko. Solving parallel equations over $\omega$-languages. Prikladnaâ diskretnaâ matematika, no. 2 (2010), pp. 117-123. http://geodesic.mathdoc.fr/item/PDM_2010_2_a11/

[1] Yevtushenko N. V., Villa T., Brayton R. K., et al., “Solution of Parallel Language Equations for Logic Synthesis”, Proceedings of ICCAD 2001, San Jose, 2001, 103–110

[2] Wang G., Mishchenko A., Brayton R. K., et al., Sequential synthesis with co-Buchi specifications, ERL Technical Report, EECS Dept., UC Berkeley, April 2006, 6 pp.

[3] Thistle J. G., Wonham W. M., “Supervision of infinte behavior of discrete-event systems”, SIAM J. Control and Optimization, 32:4 (1994), 1098–1113 | DOI | MR | Zbl

[4] Buchi J. R., “On a decision method in restricted second order arithmetic”, Z. Math. Logik Grundlag. Math., 6 (1960), 66–92 | DOI | MR

[5] Bushkov V. G., Evtushenko N. V., “Reshenie parallelnykh uravnenii dlya $\omega$-regulyarnykh yazykov”, Prikladnaya diskretnaya matematika, 2009, Prilozhenie No 1, 6–7

[6] Trakhtenbrot B. A., Barzdin Ya. M., Konechnye avtomaty (povedenie i sintez), Nauka, M., 1970, 400 pp. | MR | Zbl

[7] Mukund M., “Finite-state automata on infinite inputs”, Tutorial talk, NSTCS 6, Banasthali, Rajasthan, India, August 1996, 32 pp.

[8] Khopkroft D., Motvani R., Ulman D., Vvedenie v teoriyu avtomatov, yazykov i vychislenii, Vilyams, M., 2008, 528 pp.