Derandomizing Isolation in Space-Bounded Settings

Derandomizing Isolation in Space-Bounded Settings

We study the possibility of deterministic and randomness-efficient isolation in space-bounded models of computation: Can one efficiently reduce instances of computational problems to equivalent instances that have at most one solution? We present results for the NL-complete problem of reachability on digraphs, and for the LogCFL-complete problem of certifying acceptance on shallow semi-unbounde...

Derandomizing Isolation Lemma: A geometric approach

Derandomizing PIT for ROABP and Isolation Lemma for Special Graphs

CERTIFICATE It is certified that the work contained in the thesis entitled " Derandomizing PIT for ROABP and Isolation Lemma for Special Graphs " , by " Rohit Gurjar " , has been carried out under our supervision and that this work has not been submitted elsewhere for a degree. Synopsis Randomization is ubiquitous in computer science. Many computational problems have faster algorithms when usag...

Derandomizing the Isolation Lemma and Lower Bounds for Circuit Size

The isolation lemma of Mulmuley et al [MVV87] is an important tool in the design of randomized algorithms and has played an important role in several nontrivial complexity upper bounds. On the other hand, polynomial identity testing is a well-studied algorithmic problem with efficient randomized algorithms and the problem of obtaining efficient deterministic identity tests has received a lot of...

Bounded Geodesics in Moduli Space

In the moduli space of quadratic differentials over complex structures on a surface, we construct a set of full Hausdorff dimension of points with bounded Teichmüller geodesic trajectories. The main tool is quantitative nondivergence of Teichmüller horocycles, due to Minsky and Weiss. This has an application to billiards in rational polygons.