The problem of Identity Testing consists in given an arithmetic circuit that computes a polynomial p in a field, decide whether p is the zero polynomial. One of the first examples of probabilistic algorithms is the polynomial time randomized solution to this problem given by Schwartz and Zippel. More recently there has been considerable progress in trying to find a polynomial time deterministic...

The instance complexity of a string x with respect to a set A and time bound t, ic t (x : A), is the length of the shortest program for A that runs in time t, decides x correctly, and makes no mistakes on other strings (where \don't know" answers are permitted). Schh oning, and Watanabe states that for every recursive set A not in P and every polynomial t there is a polynomial t 0 and a constan...

We study the problem of approximating value matching polynomial on graphs with edge parameter γ, where γ takes arbitrary values in complex plane. When is a positive real, Jerrum and Sinclair showed that admits an FPRAS general graphs. For Patel Regts, building methods developed by Barvinok, FPTAS maximum degree Δ as long not negative real number less than or equal to −1/(4(Δ −1)). Our first mai...

Cooperative driving at signal-free intersections, which aims to improve safety and efficiency for connected automated vehicles, has attracted increasing interest in recent years. However, existing cooperative strategies either suffer from computational complexity or cannot guarantee global optimality. To fill this research gap, paper proposes an optimal computationally efficient strategy with t...

Weak probabilistic bisimulation on probabilistic automata can be decided by an algorithm that needs to check a polynomial number of linear programming problems encoding weak transitions. It is hence polynomial, but not guaranteed to be strongly polynomial. In this paper we show that for polynomial rational probabilistic automata strong polynomial complexity can be ensured. We further discuss co...