A finite set of functions with an EXPTIME-complete composition problem

Theoretical Computer Science

Volumn 407, Issue 1-3, 2008, Pages 330-341

  Kozik, Marcin ^a,b  

^a JAGIELLONIAN UNIVERSITY   (Poland)

^b CHARLES UNIVERSITY   (Czech Republic)

Author keywords

Clone membership problem; Composition of functions; Computational complexity

Indexed keywords

ALGEBRA; CLONING; MATRIX ALGEBRA;

CLONE MEMBERSHIP PROBLEM; COMPOSITION OF FUNCTIONS; COMPOSITION PROBLEM; COMPUTATIONAL COMPLEXITY; FINITE SETS;

SET THEORY;

EID: 53349180269     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.tcs.2008.06.057     Document Type: Article

References (16)

1. Balcázar J.~L. The complexity of searching implicit graphs. Artificial Intelligence 86 1 (1996) 171-188 MR1410132 (98a:68088)
2. Bergman C., Juedes D., and Slutzki G. Computational complexity of term-equivalence. Internat. J. Algebra Comput. 9 1 (1999) 113-128 MR1695293 (2000b:68088)
3. Burris S., and Sankappanavar H.~P. A course in universal algebra. Graduate Texts in Mathematics vol.~78 (1981), Springer-Verlag, New York MR648287 (83k:08001)
4. Elwyn Berlekamp, David Wolfe, Mathematical Go, A K Peters Ltd., Wellesley, MA, 1994, Chilling gets the last point, With a foreword by James Davies. MR1274921 (95i:90131)
5. Černý J. A remark on homogeneous experiments with finite automata. Mat.-Fyz. Časopis Sloven. Akad. Vied 14 (1964) 208-216 MR0168429 (29 #5692)
6. Chandra A.K., Kozen D.C., and Stockmeyer L.J. Alternation. J. Assoc. Comput. Mach. 28 1 (1981) 114-133 MR603186 (83g:68059)
7. Fraenkel A.S., and Lichtenstein D. Computing a perfect strategy for n × n chess requires time exponential in n. J. Combin. Theory Ser. A 31 2 (1981) 199-214 MR629595 (83b:68044)
8. Garey M.R., and Johnson D.S. Composing functions to minimize image size. SIAM J. Comput. 14 2 (1985) 500-503 MR784752 (86d:68031)
9. Jackson M., and McKenzie R. Interpreting graph colorability in finite semigroups. Internat. J. Algebra Comput. 16 1 (2006) 119-140 MR2217645 (2006m:20081)
10. Kozik M., and Kun G. The subdirectly irreducible algebras in the variety generated by graph algebras. Algebra Universalis 58 2 (2008) 229-242 MR2386530 (08B26 (68Q17))
11. Dexter Kozen, Lower bounds for natural proof systems, in: 18th Annual Symposium on Foundations of Computer Science (Providence, R.I., 1977), IEEE Comput. Sci., Long Beach, Calif., 1977, pp. 254-266, MR0495200 (58 #13931)
12. Lichtenstein D., and Sipser M. GO is polynomial-space hard. J. Assoc. Comput. Mach. 27 2 (1980) 393-401 MR567056 (81b:68052)
13. McKenzie R. The residual bound of a finite algebra is not computable. Internat. J. Algebra Comput. 6 1 (1996) 29-48
14. McKenzie R.N., McNulty G.F., and Taylor W.F. Algebras, lattices, varieties. The Wadsworth & Brooks/Cole Mathematics Series Vol. I (1987), Wadsworth & Brooks/Cole Advanced Books & Software, Monterey, CA MR883644 (88e:08001)
15. Robson J.~M. N by N checkers is Exptime complete. SIAM J. Comput. 13 2 (1984) 252-267 MR739988 (86f:90168)
16. Székely Z. Computational complexity of the finite algebra membership problem for varieties. Internat. J. Algebra Comput. 12 6 (2002) 811-823 MR1949698 (2003k:08009)