Abstract
The notion of a program over a finite semigroup has recently emerged from the work of D.A. Barrington on bounded-width branching programs [2], [3], and the joint work of D.A. Barrington and D. Thérien [4], [5]. These authors introduced programs over semigroups under the name of “non-uniform deterministic finite automata (NUDFA)”, and they studied the potential programs have in terms of recognizability of certain languages that are commonly treated in complexity theory by using families of Boolean circuits.
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References
M. Ajtai, ∑1 1 formulae on finite structures, Annals of Pure and Applied Logic 24, 1983, 1–48.
D.A. Barrington, Bounded-width polynomial-size branching programs recognize exactly those languages in NC 1, Proc. 18th A.C.M.S.T.O.C, 1986, 1-5.
D.A. Barrington, Bounded-width polynomial-size branching programs, Ph. D. thesis, M.I.T. May 1986 (Technical report TR-361, M.I.T. Lab. for Comp.Sc).
D.A. Barrington and D. Thérien, Non-uniform automata over groups, Proc. 14th I.C.A.L.P. 1987.
D.A. Barrington and D. Thérien, Finite monoids and the fine structure of NC 1, Proc. 19th A.C.M.S.T.O.C, 1987, 101-107, see also J.A.C.M. 35 (4) 1988, 941-952.
S.A. Cook, The taxonomy of problems with fast parallel algorithms, Inf. and Control 64, 1985, 2–22.
S. Eilenberg, Automata, Languages, and Machines, Vol. B, Academic Press, New York, 1976.
M. Furst, J.B. Saxe and M. Sipser, Parity, circuits, and the polynomial-time hierarchy, Math. Systems Th. 17,1984, 13-27.
G. Lallement, Semigroups and Combinatorial Applications, J. Wiley and Sons, New York, 1979.
G. Lallement, A note on languages recognized by programs over the two-element monoid, Semigroup Forum 38(3), 1989, 371–374.
A.A. Razborov, Lower bounds for the size of circuits with bounded depth with basis {&, Θ}, Matem. Zametki 41(4), 1987, 598–607, English translation Math. Notes Acad. Sci. USSR 41 (4), 1987, 333-338.
J. E. Savage, The Complexity of Computing, J. Wiley and Sons, New York, 1976.
R. Smolensky, Algebraic methods in the theory of lower bounds for Boolean circuit complexity, Proc. 19th A.C.M.S.T.O.C. 1987, 77-82.
H. Straubing, A note on non-uniform automata over groups (preprint), Boston College, Dept. of Comp. Sci., April 1987.
D. Thérien, Programs over aperiodic monoids (preprint), McGill Univ. School of Comp. Sci.
D. Thérien, P. Péladeau, Sur les langages reconnus par des groupes nilpotents (preprint), McGill Univ. School of Comp. Sci.
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Lallement, G. (1990). Programs over Finite Semigroups: An Introduction. In: Almeida, J., Bordalo, G., Dwinger, P. (eds) Lattices, Semigroups, and Universal Algebra. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-2608-1_18
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DOI: https://doi.org/10.1007/978-1-4899-2608-1_18
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