Circuits and expressions with nonassociative gates

Journal of Computer and System Sciences

Volumn 60, Issue 2, 2000, Pages 368-394

  Moore, Cristopher ^a   Thérien, Denis ^b   Lemieux, François ^c   Berman, Joshua ^d   Drisko, Arthur ^e  

^a SANTA FE INSTITUTE   (United States)

^b MCGILL UNIVERSITY   (Canada)

^c UNIVERSITÉ DU QUÉBEC À CHICOUTIMI   (Canada)

^d BINGHAMTON UNIVERSITY   (United States)

^e NATIONAL SECURITY AGENCY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOOLEAN FUNCTIONS; COMPUTATIONAL COMPLEXITY; ELECTRIC NETWORK ANALYSIS; LOGIC CIRCUITS; PROBLEM SOLVING;

NONASSOCIATIVE GROUPOIDS;

LOGIC GATES;

EID: 17044458124     PISSN: 00220000     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcss.1999.1673     Document Type: Article

References (33)

1. 1 formulae on finite structures. Ann. Pure Appl. Logic. 24:1983;1-48.
2. Albert A. A. Quasigroups I. Trans. Amer. Math. Soc. 54:1943;507-519.
3. 1. J. Comput. System Sci. 38:1989;150-164.
4. 1. Info. Proc. Lett. 32:1989;251-256.
5. 1. J. Comput. System Sci. 41:1990;274-306.
6. Bédard F., Lemieux F., McKenzie P. Extension to Barrington's M-program model. Theoret. Comput. Sci. 107:1993;31-61.
7. M. Beaudry, P. McKenzie, P. Péladeau, and D. Thérien, Circuits with monoidal gates, in Proc. STACS, 1993, pp. 555-565, Springer-Verlag, Berlin.
8. Bruck R. H. Contributions to the theory of loops. Trans. Amer. Math. Soc. 60:1946;245-354.
9. Bruck R. H. A Survey of Binary Systems. 1966;Springer-Verlag, Berlin/New York.
10. S. R. Buss, The Boolean formula value problem is in ALOGTIME, in Proc. 18th ACM Symp. on the Theory of Computing, 1987, pp. 123-131.
11. H. Caussinus and F. Lemieux, The complexity of computing over quasigroups, in Proc. 14th annual FST&TCS, 1994, pp. 36-47.
12. Chein O., Pflugfelder H. O., Smith J. D. H. Quasigroups and Loops: Theory and Applications. 1990;Heldermann-Verlag, Berlin.
13. Furst M., Saxe J. B., Sipser M. Parity, circuits, and the polynomial-time hierarchy. Math. System Theory. 17:1984;13-27.
14. Greenlaw R., Hoover H. J., Ruzzo W. L. Limits to Parallel Computation: P-Completeness Theory. 1995;Oxford University Press, Oxford.
15. Hall M. The Theory of Groups. 1976;Chelsea, New York.
16. 1. Info. Process. Lett. 29:1988;111-117.
17. Ladner R. E. The circuit value problem is LOGSPACE-complete for P. SIGACT News. 7:1975;18-20.
18. Lemieux F. Finite Groupoids and Their Applications to Computational Complexity. 1996;McGill UniversitySchool of Computer Science, Montréal.
19. Maciel A., Thérien D. Technical Report. 1995.
20. Maurer W. D., Rhodes J. L. A property of finite simple non-Abelian groups. Proc. Amer. Math. Soc. 16:1965;552-554.
21. R. McKenzie, On minimal, locally finite varieties with permuting congruence relations, preprint, 1976.
22. Moore C. Predicting non-linear cellular automata quickly by decomposing them into linear ones. Physica D. 111:1998;27-41.
23. Moore C. Quasi-linear cellular automata. Proceedings of the International Workshop on Lattice Dynamics. Physica D. 103:1997;. p. 100-132.
24. Papadimitriou C. H. Computational Complexity. 1994;Addison-Wesley, Reading.
25. Pflugfelder H. O. Quasigroups and Loops: An Introduction. 1990;Heldermann-Verlag, Berlin.
26. Razborov A. A. Lower bounds for the size of circuits of bounded depth with basis {&, ⊕}. Math. Notes Acad. Sci. USSR. 41:1987;333-338.
27. Rosenberg I. G. Completeness properties of multiple-valued logic algebras. Rhine D. C. Computer Science and Multiple-Valued Logic: Theory and Application. 1977;144-186 North-Holland, Amsterdam.
28. Ruzzo W. L. On uniform circuit complexity. J. Comput. System Sci. 22:1981;365-383.
29. R. Smolensky, Algebraic methods in the theory of lower bounds for Boolean circuit complexity, in Proc. 19th ACM Symposium on the Theory of Computing, 1987, pp. 77-82.
30. Suzuki M. Group Theory I. 1982;Springer-Verlag, Berlin/New York.
31. Szendrei A. Clones in Universal Algebra. 1986;Les Presses de L'Université de Montréal, Montréal.
32. Vesanen A. Solvable groups and loops. J. Algebra. 180:1996;862-876.
33. Weinstein M. Examples of Groups and loops. 1977;Polygonal, Passaic.