Notes on extended equation solvability and identity checking for groups
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Every finite non-nilpotent group can be extended by a term operation such that solving equations in the resulting algebra is NP-complete and checking identities is co-NP-complete. This result was firstly proven by Horváth and Szabó; the term constructed in their proof depends on the underlying group. In this paper we provide a uniform term extension that induces hard problems. In doing so we also characterize a big class of solvable, non-nilpotent groups for which extending by the commutator operation suffices.
Key words and phrasesequation solvability identity checking solvable group
Mathematics Subject Classification20F10 20F12 20D10 08A70
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The author would like to thank Attila Földvári and Gábor Horváth for their valuable feedback on earlier versions of this paper.
- 3.D. M. Barrington, P. McKenzie, C. Moore, P. Tesson, and D. Thérien, Equation satisfiability and program satisfiability for finite monoids, in: International Symposium on Mathematical Foundations of Computer Science (Bratislava, 2000), Lecture Notes in Comput. Sci., 1893, Springer (Berlin, 2000), pp. 172–181Google Scholar
- 10.G. Horváth, Functions and Polynomials over Finite Groups from the Computational Perspective, PhD thesis, University of Hertfordshire (2008)Google Scholar
- 12.G. Horváth, J. Lawrence, and R. Willard, The complexity of the equation solvability problem over finite rings, preprint, http://real.mtak.hu/28210/ (2015)
- 17.P. M. Idziak and J. Krzaczkowski, Satisfiability in multi-valued circuits, in: Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science, ACM (2018), pp. 550–558Google Scholar
- 19.D.-J. Robinson, A Course in the Theory of Groups, Springer (Berlin–Heidelberg, 1996)Google Scholar