Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-27T08:36:04.687Z Has data issue: false hasContentIssue false
  • English
  • Français

D0L sequence equivalence is in P for fixed alphabets

Published online by Cambridge University Press:  13 December 2007

Keijo Ruohonen
Keijo Ruohonen*
Affiliation:
Institute of Mathematics, Tampere University of Technology, 33101 Tampere, Finland; [email protected]
Get access

Abstract

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 $\mathbb{Z}$-rational sequences.

Keywords

D0L systemequivalence problempolynomial-time algorithm
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 42 , Issue 2 , April 2008 , pp. 361 - 374
Copyright
© EDP Sciences, 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Albert, M.H. and Lawrence, J., A proof of Ehrenfeucht's conjecture. Theoret. Comput. Sci. 41 (1985) 121–123. CrossRef
Berstel, J. and Mignotte, M., Deux problèmes décidables des suites récurrentes linéaires. Bull. Soc. Math. France 104 (1976) 175–184. CrossRef
J. Berstel and C. Reutenauer, Rational Series and Their Languages. Springer-Verlag (1988).
Blondel, V.D. and Portier, N., The presence of a zero in an integer linear recurrent sequence is NP-hard to decide. Linear Algebra Appl. 351–352 (2002) 91–98. CrossRef
Čulik II, K. and Friš, I., The decidability of the equivalence problem for D0L-systems. Inform. Control 35 (1977) 20–39. CrossRef
K. Čulik II and J. Karhumäki, 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.
Ehrenfeucht, A. and Rozenberg, G., Elementary homomorphisms and a solution of the D0L sequence equivalence problem. Theoret. Comput. Sci. 7 (1978) 169–183. CrossRef
Ehrenfeucht, A. and Rozenberg, G., On a bound for the D0L sequence equivalence problem. Theoret. Comput. Sci. 12 (1980) 339–342. CrossRef
V. Halava, T. Harju, M. Hirvensalo and J. Karhumäki, Skolem's Problem — On the Border Between Decidability and Undecidability. TUCS Technical Report No 683 (2005) (submitted).
Hansel, G., Une démonstration simple du théorème de Skolem-Mahler-Lech. Theoret. Comput. Sci. 244 (1986) 91–98. CrossRef
Honkala, J., A short solution for the HDT0L sequence equivalence problem. Theoret. Comput. Sci. 244 (2000) 267–270. CrossRef
Honkala, J., A polynomial bound for certain cases of the D0L sequence equivalence problem. Theoret. Comput. Syst. 34 (2001) 263–272. CrossRef
Honkala, J., 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. CrossRef
Honkala, J., An n 2-bound for the ultimate equivalence problem of certain D0L systems over an n-letter alphabet. J. Comput. Syst. Sci. 71 (2005) 506–519. CrossRef
Honkala, J., A new bound for the D0L sequence equivalence problem. Acta Inform. 43 (2007) 419–429. CrossRef
Karhumäki, J., On the equivalence problem for binary D0L systems. Inform. Control 50 (1981) 276–284. CrossRef
D.J. Lewis, Diophantine equations: p-adic methods, in Studies in Number Theory, edited by W.J. LeVeque. MAA Studies in Mathematics. Vol. 6 MAA (1969) 25–75.
Magnus, W., On a theorem of Marshall Hall. Ann. Math. 40 (1954) 764–768. CrossRef
G. Rozenberg and A. Salomaa, The Mathematical Theory of L Systems. Academic Press (1980).
Handbook of Formal Languages. Vols. 1–3, edited by G. Rozenberg and A. Salomaa. Springer–Verlag (1997).
K. Ruohonen, Test sets for iterated morphisms. Mathematics Report No 49. Tampere University of Technology (1986).
K. Ruohonen, 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.
Ruohonen, K., Solving equivalence of recurrent sequences in groups by polynomial manipulation. Fund. Inform. 38 (1999) 135–148.
Ruohonen, K., Explicit test sets for iterated morphisms in free monoids and metabelian groups. Theoret. Comput. Sci. 330 (2005) 171 –191. CrossRef
A. Salomaa and M. Soittola, Automata-Theoretic Aspects of Formal Power Series. Springer–Verlag (1978).
Schmidt, W.M., The zero multiplicity of linear recurrence sequences. Acta Math. 182 (1999) 243–282. CrossRef