J. Berman, A. Drisko, F. Lemieux, C. Moore, and D. Therien. Circuits and expressions with non{associative gates. In Proceedings of the 12th Annual IEEE Conference on Computational Complexity, Ulm (Germany), pages 193-203. IEEE Computer Society Press, 1997.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....word problems are uNC complete, like for instance the Boolean algebra (f0; 1g; 5] An interesting open problem might be to nd criteria for a nitely presented algebra A(F ; P) which imply that the word problem is uNC complete. For similar work in the context of nite groupoids see [4]. We should also say a few words concerning the input representation. In Theorem 1 and Corollary 1 we represent the input terms as strings over the alphabet F . This is in fact crucial for the uNC upper bounds. If we would represent input terms by their pointer representations then the ....

....a distinguished element q (namely the nal state of A) Thus the uniform membership problem for deterministic BUTAs is equivalent to the uniform expression evaluation problem for nite algebras. In the case of a xed groupoid, the complexity of the expression evaluation problem was considered in [4]. Table 1 summarizes the complexity results for tree automata shown in this paper. Table 1. Complexity results for tree automata det. TDTA det. BUTA TDTA (BUTA) membership uNC complete uniform membership L complete LOGDCFL LOGCFL complete Acknowledgments I would like to thank the ....

J. Berman, A. Drisko, F. Lemieux, C. Moore, and D. Therien. Circuits and expressions with non{associative gates. In Proceedings of the 12th Annual IEEE Conference on Computational Complexity, Ulm (Germany), pages 193-203. IEEE Computer Society Press, 1997.

.... 2R1,beaudry dmi.usherb.ca z School of Computer Science, McGill University, 3480 rue University, Montr eal (Qc) Canada, H3A 2A7, lemieux cs.mcgill.ca x Corresponding author: School of Computer Science, McGill University, 3480 rue University, Montr eal (Qc) Canada, H3A 2A7, denis cs.mcgill.ca [7, 8, 1, 6], consists of loops, i.e. groupoids with an identity and for which every row and every column of the multiplication table contains every element. In [9] it was proved that any language recognized by a finite loop must be regular. The main result of our paper gives an exact characterization of ....

....could be related to such natural class of languages as the regular open languages. Our generalization of the block product yields a loop decomposition that shows that absence of associativity does not necessarily imply absence of structure. This is also confirmed by other recent works, such as [6]. We strongly believe that a better understanding of non associative algebras, in particular finite groupoids, could have important consequences in language theory and computational complexity. ....

J. Berman, A. Drisko, F. Lemieux, C. Moore, and D. Th'erien, Circuits and Expressions with Non-Associative Gates, Submitted to 12th Annual Conference on Computational Complexity (CCC'97)

....We note that of the 24 non isomorphic quasigroups of order 4, for example, 14 are polyabelian and have CAs in ACC 0 . The other 10 are capable of expressing arbitrary Boolean functions and so their Circuit Value problem and, we conjecture, their CA Prediction problem is P complete [26]. Acknowledgements. I am grateful to Daniel Ashlock, Martin Beaudry, Joshua Berman, Arthur Drisko, Chris Hillman, Derek Holt, Jim Hoover, Peter Johnson, Werner Nickel, Mats Nordahl, Tom Richardson, John Rickard, David Rusin, V. Vinay, and Ross Willard for helpful communications, and to Elizabeth ....

J. Berman, A. Drisko, F. Lemieux, C. Moore and D. Th'erien, "Circuits and expressions with non-associative gates." To appear in the 12th Annual IEEE Conference on Computational Complexity.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC