Abstract
We extend the well known characterization of the arithmetic circuit class VP ws as the class of polynomials computed by polynomial size arithmetic branching programs to other complexity classes. In order to do so we add additional memory to the computation of branching programs to make them more expressive. We show that allowing different types of memory in branching programs increases the computational power even for constant width programs. In particular, this leads to very natural and robust characterizations of VP and VNP by branching programs with memory.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Barrington, D.A.: Bounded-width polynomial-size branching programs recognize exactly those languages in NC1. Journal of Computer and System Sciences 38(1), 150–164 (1989)
Ben-Or, M., Cleve, R.: Computing algebraic formulas using a constant number of registers. SIAM J. Comput. 21(1), 54–58 (1992)
Brent, R.P.: The complexity of multiple-precision arithmetic. In: Brent, R.P., Andersson, R.S. (eds.) The Complexity of Computational Problem Solving, pp. 126–165. Univ. of Queensland Press (1976)
Briquel, I., Koiran, P.: A dichotomy theorem for polynomial evaluation. In: Královič, R., Niwiński, D. (eds.) MFCS 2009. LNCS, vol. 5734, pp. 187–198. Springer, Heidelberg (2009)
Bürgisser, P.: Completeness and reduction in algebraic complexity theory. Springer (2000)
Kintali, S.: Realizable paths and the NL vs L problem. Electronic Colloquium on Computational Complexity (ECCC) 17, 158 (2010)
Koiran, P.: Arithmetic circuits: The chasm at depth four gets wider. Theor. Comput. Sci. 448, 56–65 (2012)
Malod, G., Portier, N.: Characterizing Valiant’s algebraic complexity classes. J. Complexity 24(1), 16–38 (2008)
Mengel, S.: Arithmetic Branching Programs with Memory, arXiv:1303.1969 (2013)
Nisan, N.: Lower bounds for non-commutative computation. In: Proceedings of the Twenty-Third Annual ACM Symposium on Theory of Computing, p. 418. ACM (1991)
Skyum, S., Valiant, L.G.: A complexity theory based on boolean algebra. J. ACM 32(2), 484–502 (1985)
Toda, S.: Classes of arithmetic circuits capturing the complexity of computing the determinant. IEICE Transactions on Information and Systems 75(1), 116–124 (1992)
Valiant, L.G., Skyum, S., Berkowitz, S., Rackoff, C.: Fast parallel computation of polynomials using few processors. SIAM J. Comput. 12(4), 641–644 (1983)
Valiant, L.G.: Completeness classes in algebra. In: Proceedings of the Eleventh Annual ACM Symposium on Theory of Computing, pp. 249–261. ACM (1979)
Weber, V., Schwentick, T.: Dynamic complexity theory revisited. Theory Comput. Syst. 40(4), 355–377 (2007)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Mengel, S. (2013). Arithmetic Branching Programs with Memory. In: Chatterjee, K., Sgall, J. (eds) Mathematical Foundations of Computer Science 2013. MFCS 2013. Lecture Notes in Computer Science, vol 8087. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40313-2_59
Download citation
DOI: https://doi.org/10.1007/978-3-642-40313-2_59
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-40312-5
Online ISBN: 978-3-642-40313-2
eBook Packages: Computer ScienceComputer Science (R0)