OPTIMAL POLYNOMIAL LOWER BOUNDS FOR THE EXPONENTIAL FUNCTION

Some tight polynomial-exponential lower bounds for an exponential function

This note is devoted to new sharp lower bounds for exp(x). We first introduce and study a new lower bound defined with polynomial of degree 2 and exponential (or hyperbolic) functions. Then we propose two improvements of this lower bound by using two different approaches; the first approach consists in adding well-chosen polynomial term to it, whereas the second approach aims to transform it fo...

Polynomial Degree Lower Bounds

We show that an oracle A that contains either 1/4 or 3/4 of all strings of length n can be used to separate EQP from the counting classes MODpkP, where p is a prime. Our proof makes use of the degree of a representing polynomial over Zpk . We show a linear lower bound on the degree of this polynomial. We also show an upper bound of O(n logp ) on the degree over the ring Zm, whenever m is a squa...

Exponential Lower Bounds for Policy Iteration

We study policy iteration for infinite-horizon Markov decision processes. It has recently been shown policy iteration style algorithms have exponential lower bounds in a two player game setting. We extend these lower bounds to Markov decision processes with the total reward and average-reward optimality criteria.

Nonuniform Lower Bounds for Exponential Time Classes

Some lower bounds for the $L$-intersection number of graphs

‎For a set of non-negative integers~$L$‎, ‎the $L$-intersection number of a graph is the smallest number~$l$ for which there is an assignment of subsets $A_v subseteq {1,dots‎, ‎l}$ to vertices $v$‎, ‎such that every two vertices $u,v$ are adjacent if and only if $|A_u cap A_v|in L$‎. ‎The bipartite $L$-intersection number is defined similarly when the conditions are considered only for the ver...