In this paper, we formalize two stepwise approaches, based on pseudo-random generators, for proving P 6= NP and its arithmetic analog: Permanent requires superpolynomial sized arithmetic circuits.

2008 49th Annual IEEE Symposium on Foundations ofâ€¦

2008

We show that proving exponential lower bounds on depth four arithmetic circuits imply exponential lower bounds for unrestricted depth arithmetic circuits. In other words, for exponential sizedâ€¦ (More)

A finite state Markov chain M is often viewed as a probabilistic transition system. An alternative view - which we follow here - is to regard M as a linear transform operating on the space ofâ€¦ (More)

We give a simple and new randomized primality testing algorithm by reducing primality testing for number <i>n</i> to testing if a specific univariate identity over <i>Z<sub>n</sub></i> holds.We alsoâ€¦ (More)

We study the class of lazy linear hybrid automata with finite precision. The key features of this class are: â€“ The observation of the continuous state and the rate changes associated with modeâ€¦ (More)

We study the problem of expressing permanents of matrices as determinants of (possibly larger) matrices. This problem has close connections to the complexity of arithmetic computations: theâ€¦ (More)

We investigate the computational complexity of the Boolean Isomorphism problem (BI): on input of two Boolean formulas F and G decide whether there exists a permutation of the variables of G such thatâ€¦ (More)