A Note on Amortized Branching Program Complexity

Author Aaron Potechin

Thumbnail PDF


  • Filesize: 0.49 MB
  • 12 pages

Document Identifiers

Author Details

Aaron Potechin

Cite AsGet BibTex

Aaron Potechin. A Note on Amortized Branching Program Complexity. In 32nd Computational Complexity Conference (CCC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 79, pp. 4:1-4:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


In this paper, we show that while almost all functions require exponential size branching programs to compute, for all functions f there is a branching program computing a doubly exponential number of copies of f which has linear size per copy of f. This result disproves a conjecture about non-uniform catalytic computation, rules out a certain type of bottleneck argument for proving non-monotone space lower bounds, and can be thought of as a constructive analogue of Razborov's result that submodular complexity measures have maximum value O(n).
  • branching programs
  • space complexity
  • amortization


  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    PDF Downloads


  1. Laszlo Babai, Noam Nisan, and Mario Szegedy. Multiparty Protocols, Pseudorandom Generators for Logspace, and Time-Space trade-offs. Journal of Computer and System Sciences, 45:204-232, 1992. Google Scholar
  2. Harry Buhrman, Richard Cleve, Michal Koucký, Bruno Loff, and Florian Speelman. Computing with a full memory: catalytic space. In 46th Annual Symposium on the Theory of Computing (STOC 2014), pages 857-866, 2014. URL: http://dx.doi.org/10.1145/2591796.2591874.
  3. Siu Man Chan and Aaron Potechin. Tight Bounds for Monotone Switching Networks via Fourier Analysis. Theory of Computing, 10:389-419, 2014. URL: http://dx.doi.org/10.1145/2213977.2214024.
  4. Stephen Cook, Jeff Edmonds, Venkatesh Medabalimi, and Toniann Pitassi. Lower Bounds for Nondeterministic Semantic Read-Once Branching Programs. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016), volume 55 of LIPIcs, pages 36:1-36:13. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2016. URL: http://dx.doi.org/10.4230/LIPIcs.ICALP.2016.36.
  5. Vincent Girard, Michal Koucký, and Pierre McKenzie. Nonuniform catalytic space and the direct sum for space, 2015. URL: https://eccc.weizmann.ac.il/report/2015/138/.
  6. Oleg Lupanov. The synthesis of contact circuits. Doklady Akademii Nauk SSSR, 119:23-26, 1958. Google Scholar
  7. William Masek. A fast algorithm for the string editing problem and decision graph complexity. Master’s thesis, MIT, 1976. Google Scholar
  8. E. I. Nechiporuk. On a Boolean function. Soviet Mathematics Doklady, 7(4):999-1000, 1966. Google Scholar
  9. Alexander Razborov. Lower bounds for deterministic and nondeterministic branching programs. In Proceedings of the 8th International Symposium on Fundamentals of Computation Theory (FCT), volume 529 of LNCS, pages 47-60, 1991. Google Scholar
  10. Alexander Razborov. On submodular complexity measures. In Proceedings of the London Mathematical Society symposium on Boolean function complexity, pages 76-83, 1992. Google Scholar
  11. Claude Shannon. The synthesis of two-terminal switching circuits. Bell System Technical Journal, 28:59-98, 1949. Google Scholar
  12. Dietmar Uhlig. On the synthesis of self-correcting schemes for functional elements with a small number of reliable elements. In Mathematical Notes of the Academy of Sciences of the USSR, volume 16, pages 558-562, 1974. Google Scholar
  13. Dietmar Uhlig. Networks computing boolean functions for multiple input values. In Proceedings of the London Mathematical Society Symposium on Boolean Function Complexity, pages 165-173, 1992. Google Scholar
  14. Ingo Wegener. On the complexity of branching programs and decision trees for clique functions. Journal of the Association for Computing Machinery (JACM), 35(2):389-419, 1988. URL: http://dx.doi.org/10.1145/42282.46161.
  15. Stanislav Zak. An exponential lower bound for one-time-only branching programs. In Proceedings of the Mathematical Foundations of Computer Science (MFCF), pages 562-566, 1984. Google Scholar
Questions / Remarks / Feedback

Feedback for Dagstuhl Publishing

Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail