The complexity of functions on lattices

Theoretical Computer Science

Volumn 246, Issue 1-2, 2000, Pages 195-225

  Sander, J W ^a   Tijdeman, R ^b  

^a LEIBNIZ UNIVERSITY HANNOVER   (Germany)

^b LEIDEN UNIVERSITY   (Netherlands)

Author keywords

Lattices; Low complexity; Patterns; Periodicity

Indexed keywords

EID: 0000112667     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-3975(99)00078-X     Document Type: Article

References (31)

1. E. Altman, B. Gaujal, A. Hordijk, Admission control in stochastic event graphs, Report TW-97-06, Leiden University, November 1997.
2. A. Amir, G. Benson, Two-dimensional periodicity in rectangular arrays, SIAM J. Comput. 27 (1998) 90-106.
3. P. Arnoux, C. Mauduit, I. Shiokawa, J.-I. Tamura, Rauzy's conjecture on billards in the cube, Tokyo J. Math. 17 (1994) 211-218.
4. Yu. Baryshnikow, Complexity of trajectories in rectangular billards, Comm. Math. Phys. 174 (1995) 43-56.
5. J. Berstel, Recent results in Sturmian words, in: Dassow, Rozenberg, Salomaa (Eds.), Developments in Language Theory II, World Scientific, Singapore, 1996, pp. 13-24.
6. V. Berthé, L. Vuillon, Tilings and rotations, preprint.
7. N.G. de Bruijn, Algebraic theory of Penrose's nonperiodic tilings of the plane, I, II, Nederl. Akad. Wetensch. Indag. Math. 43 (1981) 39-52, 53-66.
8. N.G. de Bruijn, Updown generation of Penrose patterns, Indag. Math. (N.S.) 1 (1990) 201-220.
9. S. Bullett, P. Sentenac, Ordered orbits of the shift, square roots, and the devil's staircase, Math. Proc. Cambridge Philos. Soc. 115 (1994) 451-481.
10. J. Cassaigne, Oral communication.
11. E.M Coven, Sequences with minimal block growth, II, Math. Systems Theory 8 (1974/75) 376-382.
12. E.M. Coven, G.A. Hedlund, Sequences with minimal block growth, Math. Systems Theory 7 (1973) 138-153.
13. S. Dulucq, D. Gouyou-Beauchamps, Sur les facteurs des suites de Sturm, Theoret. Comput. Sci. 71 (1990) 381-400.
14. A.S. Fraenkel, Complementing and exactly covering sequences, J. Combin. Theory Ser. A 14 (1973) 8-20.
15. A.S. Fraenkel, R. Holzman, Gap problems for integer part and fractional part sequences, J. Number Theory 50 (1995) 66-86.
16. B. Gaujal, Optimal allocation sequences of two processes sharing a resource, Discrete Event Dynamic Systems, 1999, to appear.
17. R.L. Graham, Covering the positive integers by disjoint sets of the form {[nα + β]: n = 1, 2, . . .}, J. Combin. Theory Ser. A 15 (1973) 354-358.
18. S. Ito, M. Ohtsuki, Parallelogram tilings and Jacobi-Perron algorithm, Tokyo J. Math. 17 (1994) 33-58.
19. C.G. Lekkerkerker, Geometry of Numbers, North-Holland, Amsterdam, London, 1969.
20. F. Mignosi, Sturmian words and ambiguous context-free languages, Internat. J. Found. Comput. Sci. 1 (1990) 309-323.
21. F. Mignosi, On the number of factors of Sturmian words, Theoret. Comput. Sci. 82 (1991) 71-84.
22. i], i = 1, 2, Proc. Jpn Acad. Ser. A Math. Sci. 58 (1982) 269-271.
23. M. Morse, G.A. Hedlund, Symbolic dynamics, Amer. J. Math. 60 (1938) 815-866.
24. M. Morse, G.A. Hedlund, Symbolic dynamics II. Sturmian trajectories, Amer. J. Math. 62 (1940) 1-42.
25. M.E. Paul, Minimal symbolic flows having minimal block growth, Math. Systems Theory 8 (1974/75) 309-315.
26. G. Rauzy, Mots infinis en arithmétique, Automata on infinite words, Lecture Notes in Computer Science, vol. 192, Springer, Berlin, 1985, pp. 165-171.
27. J.W. Sander, R. Tijdeman, The rectangle complexity of functions on two-dimensional lattices, Theoret. Comput. Sci., to appear.
28. M. Senechal, Quasicrystals and geometry, Cambridge University Press, Cambridge, 1995.
29. C. Series, The geometry of Markoff numbers, Math. Intelligencer 7 (1985) 20-29.
30. R.J. Simpson, Disjoint covering systems of rational Beatty sequences, Discrete Math. 92 (1991) 361-369.
31. L. Vuillon, Combinatoire des motifs d'une suite sturmienne bidimensionelle, Theoret. Comput. Sci., to appear.