A new algorithm is presented for the D0L sequence equivalence problem which, when the alphabets are fixed, works in time polynomial in the rest of the input data. The algorithm uses a polynomial encoding of words and certain well-known properties of -rational sequences.
@article{ITA_2008__42_2_361_0,
author = {Ruohonen, Keijo},
title = {D0L sequence equivalence is in $P$ for fixed alphabets},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
volume = {42},
year = {2008},
pages = {361-374},
doi = {10.1051/ita:2007037},
mrnumber = {2401267},
zbl = {1144.68037},
language = {en},
url = {http://dml.mathdoc.fr/item/ITA_2008__42_2_361_0}
}
Ruohonen, Keijo. D0L sequence equivalence is in $P$ for fixed alphabets. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 42 (2008) pp. 361-374. doi : 10.1051/ita:2007037. http://gdmltest.u-ga.fr/item/ITA_2008__42_2_361_0/
[1] and , A proof of Ehrenfeucht's conjecture. Theoret. Comput. Sci. 41 (1985) 121-123. | MR 841029 | Zbl 0602.68066
[2] and , Deux problèmes décidables des suites récurrentes linéaires. Bull. Soc. Math. France 104 (1976) 175-184. | Numdam | MR 414475 | Zbl 0329.10009
[3] and , Rational Series and Their Languages. Springer-Verlag (1988). | MR 971022 | Zbl 0668.68005
[4] and , The presence of a zero in an integer linear recurrent sequence is NP-hard to decide. Linear Algebra Appl. 351-352 (2002) 91-98. | MR 1917474 | Zbl 1007.93047
[5] and , The decidability of the equivalence problem for D0L-systems. Inform. Control 35 (1977) 20-39. | MR 449030 | Zbl 0365.68074
[6] and , A new proof for the D0L sequence equivalence problem and its implications, in The Book of L, edited by G. Rozenberg and A. Salomaa. Springer-Verlag (1986) 63-74. | Zbl 0586.68066
[7] and , Elementary homomorphisms and a solution of the D0L sequence equivalence problem. Theoret. Comput. Sci. 7 (1978) 169-183. | MR 509015 | Zbl 0407.68085
[8] and , On a bound for the D0L sequence equivalence problem. Theoret. Comput. Sci. 12 (1980) 339-342. | MR 589315 | Zbl 0456.68085
[9] , , and , Skolem's Problem - On the Border Between Decidability and Undecidability. TUCS Technical Report No 683 (2005) (submitted).
[10] , Une démonstration simple du théorème de Skolem-Mahler-Lech. Theoret. Comput. Sci. 244 (1986) 91-98. | MR 847905 | Zbl 0605.10007
[11] , A short solution for the HDT0L sequence equivalence problem. Theoret. Comput. Sci. 244 (2000) 267-270. | MR 1774399 | Zbl 0945.68104
[12] , A polynomial bound for certain cases of the D0L sequence equivalence problem. Theoret. Comput. Syst. 34 (2001) 263-272. | MR 1823124 | Zbl 0988.68106
[13] , The equivalence problem of polynomially bounded D0L systems - a bound depending only on the size of the alphabet. Theoret. Comput. Syst. 36 (2003) 89-103. | MR 1941845 | Zbl 1039.68067
[14] , An -bound for the ultimate equivalence problem of certain D0L systems over an -letter alphabet. J. Comput. Syst. Sci. 71 (2005) 506-519. | MR 2178078 | Zbl 1082.68051
[15] , A new bound for the D0L sequence equivalence problem. Acta Inform. 43 (2007) 419-429. | MR 2282860 | Zbl 1106.68060
[16] , On the equivalence problem for binary D0L systems. Inform. Control 50 (1981) 276-284. | MR 691593 | Zbl 0497.68048
[17] , Diophantine equations: -adic methods, in Studies in Number Theory, edited by W.J. LeVeque. MAA Studies in Mathematics. Vol. 6 MAA (1969) 25-75. | MR 241359 | Zbl 0218.10035
[18] , On a theorem of Marshall Hall. Ann. Math. 40 (1954) 764-768. | Zbl 0022.31403
[19] and , The Mathematical Theory of L Systems. Academic Press (1980). | MR 561711 | Zbl 0508.68031
[20] Handbook of Formal Languages. Vols. 1-3, edited by G. Rozenberg and A. Salomaa. Springer-Verlag (1997). | MR 1469992 | Zbl 0866.68057
[21] , Test sets for iterated morphisms. Mathematics Report No 49. Tampere University of Technology (1986).
[22] , Equivalence problems for regular sets of word morphisms, in The Book of L, edited by G. Rozenberg and A. Salomaa. Springer-Verlag (1986) 393-401. | Zbl 0612.68052
[23] , Solving equivalence of recurrent sequences in groups by polynomial manipulation. Fund. Inform. 38 (1999) 135-148. | MR 1718116 | Zbl 0935.68134
[24] , Explicit test sets for iterated morphisms in free monoids and metabelian groups. Theoret. Comput. Sci. 330 (2005) 171 -191. | MR 2112773 | Zbl 1078.68094
[25] and , Automata-Theoretic Aspects of Formal Power Series. Springer-Verlag (1978). | MR 483721 | Zbl 0377.68039
[26] , The zero multiplicity of linear recurrence sequences. Acta Math. 182 (1999) 243-282. | MR 1710183 | Zbl 0974.11013