Hardness of Function Composition for Semantic Read once Branching Programs

Jeff Edmonds, Venkatesh Medabalimi, Toniann Pitassi, Marc Herbstritt
2018 Computational Complexity Conference  
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 Ω(h) , i.e space Ω(h log k). Our lower bound nearly
more » ... the natural upper bound which follows the best strategy for blackwhite 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.
doi:10.4230/lipics.ccc.2018.15 dblp:conf/coco/EdmondsMP18 fatcat:xhitioiy3nbella7iewr3wkofy