# A new algebraic invariant for weak equivalence of sofic subshifts

RAIRO - Theoretical Informatics and Applications (2008)

- Volume: 42, Issue: 3, page 481-502
- ISSN: 0988-3754

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topChaubard, Laura, and Costa, Alfredo. "A new algebraic invariant for weak equivalence of sofic subshifts." RAIRO - Theoretical Informatics and Applications 42.3 (2008): 481-502. <http://eudml.org/doc/250340>.

@article{Chaubard2008,

abstract = {
It is studied how taking the inverse image
by a sliding block code affects the syntactic semigroup of a sofic
subshift. The main tool are ζ-semigroups, considered as
recognition structures for sofic subshifts.
A new algebraic invariant is obtained for
weak equivalence of sofic subshifts, by
determining which classes of sofic subshifts
naturally defined by pseudovarieties of finite semigroups are closed
under weak equivalence. Among such classes are the classes of almost
finite type subshifts and aperiodic subshifts.
The algebraic invariant is compared with other robust conjugacy
invariants.
},

author = {Chaubard, Laura, Costa, Alfredo},

journal = {RAIRO - Theoretical Informatics and Applications},

keywords = {Sofic subshift; conjugacy; weak equivalence; ζ-semigroup; pseudovariety.; sofic subshift; -semigroup; pseudovarieties of finite semigroups},

language = {eng},

month = {6},

number = {3},

pages = {481-502},

publisher = {EDP Sciences},

title = {A new algebraic invariant for weak equivalence of sofic subshifts},

url = {http://eudml.org/doc/250340},

volume = {42},

year = {2008},

}

TY - JOUR

AU - Chaubard, Laura

AU - Costa, Alfredo

TI - A new algebraic invariant for weak equivalence of sofic subshifts

JO - RAIRO - Theoretical Informatics and Applications

DA - 2008/6//

PB - EDP Sciences

VL - 42

IS - 3

SP - 481

EP - 502

AB -
It is studied how taking the inverse image
by a sliding block code affects the syntactic semigroup of a sofic
subshift. The main tool are ζ-semigroups, considered as
recognition structures for sofic subshifts.
A new algebraic invariant is obtained for
weak equivalence of sofic subshifts, by
determining which classes of sofic subshifts
naturally defined by pseudovarieties of finite semigroups are closed
under weak equivalence. Among such classes are the classes of almost
finite type subshifts and aperiodic subshifts.
The algebraic invariant is compared with other robust conjugacy
invariants.

LA - eng

KW - Sofic subshift; conjugacy; weak equivalence; ζ-semigroup; pseudovariety.; sofic subshift; -semigroup; pseudovarieties of finite semigroups

UR - http://eudml.org/doc/250340

ER -

## References

top- J. Almeida, Finite semigroups and universal algebra, World Scientific, Singapore (1995), English translation. Zbl0757.08001
- M.-P. Béal, F. Fiorenzi, and D. Perrin, A hierarchy of shift equivalent sofic shifts. Theoret. Comput. Sci.345 (2005) 190–205. Zbl1079.68048
- M.-P. Béal, F. Fiorenzi, and D. Perrin, The syntactic graph of a sofic shift is invariant under shift equivalence. Int. J. Algebra Comput.16 (2006), 443–460. Zbl1098.68062
- M.-P. Béal and D. Perrin, A weak equivalence between shifts of finite type. Adv. Appl. Math.29 (2002) 2, 162–171. Zbl1018.37007
- D. Beauquier, Minimal automaton for a factorial transitive rational language. Theoret. Comput. Sci.67 (1985), 65–73. Zbl0679.68110
- F. Blanchard and G. Hansel, Systèmes codés. Theoret. Comput. Sci.44 (1986), 17–49. Zbl0601.68056
- M. Boyle and W. Krieger, Almost markov and shift equivalent sofic systems, Proceedings of Maryland Special Year in Dynamics 1986–87 (J.C. Alexander, ed.). Lect. Notes Math. 1342 (1988), pp. 33–93.
- M.-P. Béal, Codage symbolique, Masson (1993).
- O. Carton, Wreath product and infinite words. J. Pure Appl. Algebra153 (2000), 129–150. Zbl0987.20034
- L. Chaubard, L`équivalence faible des systèmes sofiques, Master's thesis, LIAFA, Université Paris VII, July 2003, Rapport de stage de DEA.
- A. Costa, Pseudovarieties defining classes of sofic subshifts closed under taking shift equivalent subshifts. J. Pure Appl. Algebra209 (2007), 517–530. Zbl1130.20043
- S. Eilenberg, Automata, languages and machines, vol. B, Academic Press, New York, 1976. Zbl0359.94067
- R. Fischer, Sofic systems and graphs. Monatsh. Math.80 (1975), 179–186. Zbl0314.54043
- G. A. Hedlund, Endomorphims and automorphisms of the shift dynamical system. Math. Syst. Theor.3 (1969), 320–375. Zbl0182.56901
- W. Krieger, On sofic systems. i. Israel J. Math.48 (1984), 305–330. Zbl0573.54032
- D. Lind and B. Marcus, An introduction to symbolic dynamics and coding, Cambridge University Press, Cambridge (1996). Zbl1106.37301
- M. Nasu, Topological conjugacy for sofic systems. Ergod. Theory Dyn. Syst.6 (1986), 265–280. Zbl0607.54026
- D. Perrin and J.-E. Pin, Infinite words, Pure and Applied Mathematics, No. 141, Elsevier, London, 2004. Zbl1094.68052
- J.-E. Pin, Varieties of formal languages, Plenum, London (1986), English translation.
- J.-E. Pin, Syntactic semigroups, Handbook of Language Theory (G. Rozenberg and A. Salomaa, eds.), Springer (1997).

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