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Hardness of Function Composition for Semantic Read once Branching Programs

Authors Jeff Edmonds , Venkatesh Medabalimi , Toniann Pitassi



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Jeff Edmonds
  • York University, 4700 Keele Street, Toronto, CANADA
Venkatesh Medabalimi
  • University of Toronto, 10 King’s College Road, Toronto, CANADA
Toniann Pitassi
  • University of Toronto, 10 King’s College Road, Toronto, CANADA, and Institute for Advanced Study, Princeon NJ

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Jeff Edmonds, Venkatesh Medabalimi, and Toniann Pitassi. Hardness of Function Composition for Semantic Read once Branching Programs. In 33rd Computational Complexity Conference (CCC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 102, pp. 15:1-15:22, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)
https://doi.org/10.4230/LIPIcs.CCC.2018.15

Abstract

In this work, we study time/space trade-offs for function composition. We prove asymptotically optimal lower bounds for function composition in the setting of nondeterministic read once branching programs, for the syntactic model as well as the stronger semantic model of read-once nondeterministic computation. We prove that such branching programs for solving the tree evaluation problem over an alphabet of size k requires size roughly k^{Omega(h)}, i.e space Omega(h log k). Our lower bound nearly matches the natural upper bound which follows the best strategy for black-white pebbling the underlying tree. While previous super-polynomial lower bounds have been proven for read-once nondeterministic branching programs (for both the syntactic as well as the semantic models), we give the first lower bounds for iterated function composition, and in these models our lower bounds are near optimal.

Subject Classification

ACM Subject Classification
  • Theory of computation → Complexity classes
Keywords
  • Branching Programs
  • Function Composition
  • Time-Space Tradeoffs
  • Semantic Read Once
  • Tree Evaluation Problem

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