On Automata Accepting Biordered Set Languages and its Properties
DOI:
https://doi.org/10.26713/cma.v12i3.1650Keywords:
Elementary automata, finitely bsl, nice automata.Abstract
Here we introduce the notion of finite state machines which accepts biordered set languages termed as nice automata. We begin by a basic type of automata termed as elementary automata which accepts elementary languages and give a characterization for the same. By considering the biordered set languages recognized by finite monoids we call them as finitely bsl, we see that the language L is finitely bsl if and only if there exist a nice automaton A such that L = L(A). Also we see that product is the only operation which is closed in the class of nice automata.
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References
R. Broeksteeg, Concept of variety for regular biordered sets, Semigroup Forum 49 (1994), 335 { 3482, doi:10.1007/BF02573495.
D. Easdown, Biordered sets come from semigroups, J. Algebra 96(2) (1985), 581 { 591, doi:doi.org/10.1016/0021-8693(85)90028-6.
D. Easdown, M. Sapir, M. Volkov, Periodic elements of the free idempotent generated semigroup on a biordered set, International Journal of Algebra and computation 20 (2010), 189 { 194, doi:10.1142/S0218196710005583
Y. Dandan and V. Gould, Free idempotent generated semigroups over bands and biordered sets with trivial products, International Journal of Algebra and computation 26 (2016), 473 { 507, doi:10.1142/S021819671650020X
S. Eilenberg, Automata, Languages and Machines Vol. A Academic Press, London (1974).
T. E. Hall, Identities for existence varieties of regular semigroups, Bulletin of Australian Mathematical Society 40 (1989), 59 { 77, doi:10.1017/S000497270000349X
P. M. Higgins, Techniques of Semigroup Theory, The Clarendon Press, New York (1992).
J. M. Howie, Fundamentals of Semigroup Theory, Oxford University Press, London (1995).
S. C. Kleene, Representation of events in nerve nets and nite automaton in Automata studies", C. E. Shannon and J. McCarthy(Eds.), Princeton University Press, (1956), 3 { 41, doi:10.1515/9781400882618-002
K. S. S. Nambooripad, Structure of regular semigroup. I, Memoirs of American Mathematical Society 22(224) (1979), doi:dx.doi.org/10.1090/memo/0224
J. E. Pin, Mathematical foundations of automata Theory https://www.irif.fr/~jep//PDF/MPRI/MPRI.pdf, 2020.
M. O. Rabin and D. Scott, Finite automata and their decision problems, IBM Journal 3(2) (1959), 114 { 125, doi:10.1147/rd.32.0114
A. R. Rajan and P. Ramesh Kumar, Biordered set languages, Indian J. pure appl. Math. 27(4) (1996) 343 { 355.
P. Ramesh Kumar, Biorder relations in languages, Proc. of the Symposium of Graph Theory and Applications, Kochi, Kerala, (1991), 99 { 104.
P. Ramesh Kumar and Jino Nainan, On biordered set languages and ideal languages, Proceedings of the International Conference on Semigroups, Algebras and Applications(ICSAA-2015), 2015, 57 { 63.
M. B. Szendrei, Structure theory of regular semigroups, Semigroup Forum 100(1) (2019), 119 { 140, doi:10.1007/s00233-019-10055-8
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