Biography

My main research focus is the size complexity of two-way finite automata (2FA). These are finite automata whose input head can move in both directions; equivalently, these are Turing machines which cannot write on their tape.

Since 2001, I have worked extensively on the so-called Sakoda-Sipser conjecture. This states that, for every n, there exists a non-deterministic 2FA with n states such that the number of states in the smallest deterministic 2FA which is equivalent to it is super-polynomial in n. Posed in the early 70s, this conjecture can be seen as a miniature version of our deep open questions on the power of non-determinism (P versus NP; L versus NL). In my strongest result, I have confirmed the statement in the special case where the number of times that the deterministic 2FA can reverse its input head is sublinear in the length of the input (Information and Computation, 2013).

Since 2009, I have also been working on a general size-complexity theory for 2FA, which I like to call "Minicomplexity". Here, the aim is to show that several of the properties of computation that we observe in standard Complexity Theory emerge already when the computational model and resource of interest is (not the much more powerful Turing machine and its running time, but) the 2FA and its size (Journal of Automata, Languages, and Combinatorics, 2012). As an example, one can prove a connection between 2FA and logical formulas analogous to Fagin's Theorem (Developments in Language Theory, 2012).

I am currently an Associate Teaching Professor at Carnegie Mellon University in Qatar.