Residence Toronto, Canada Role Mathematician Name Toniann Pitassi | Alma mater University of Toronto Doctoral advisor Stephen Cook | |

Education University of Toronto, Pennsylvania State University Fields Mathematics, Computer Science | ||

Institutions University of Toronto |

## Toniann pitassi proof complexity tutorial i

**Toniann Pitassi** is a Canadian and American mathematician and computer scientist specializing in computational complexity theory.

## Contents

- Toniann pitassi proof complexity tutorial i
- Tutorial on proof complexity part i toniann pitassi
- Academic career
- Research
- Selected publications
- References

## Tutorial on proof complexity part i toniann pitassi

## Academic career

A native of Pittsburgh, Pitassi earned bachelor's and master's degrees at Pennsylvania State University before moving to the University of Toronto for her doctoral studies; she earned her Ph.D. in 1992 from Toronto under the supervision of Stephen Cook. After postdoctoral studies at the University of California, San Diego and faculty positions at the University of Pittsburgh and University of Arizona, she returned to Toronto in 2001, and is now a professor in the University of Toronto Department of Computer Science and University of Toronto Department of Mathematics.

She was an invited speaker at International Congress of Mathematicians in Berlin in 1998. She was the program chair for the 2012 Symposium on Theory of Computing.

## Research

Pitassi's research has largely focused on proof complexity, a branch of computational complexity theory that seeks upper and lower bounds on the lengths of mathematical proofs of logical propositions within various formalized proof systems. The goal of this study is to use these bounds to understand both the time complexity of proof-finding procedures, and the relative strengths of different proof systems.

Research contributions that she has made in this area include exponential lower bounds for Frege proofs of the pigeonhole principle, exponential lower bounds for the cutting-plane method applied to propositions derived from the maximum clique problem, exponential lower bounds for resolution proofs of dense random 3-satisfiability instances, and subexponential upper bounds for the same dense random instances using the Davis–Putnam algorithm. With Paul Beame, she also wrote a survey of proof complexity.

## Selected publications

*Computational Complexity*,

**3**(2): 97–140, MR 1233662, doi:10.1007/BF01200117 .

*Proceedings of the 37th Annual Symposium on Foundations of Computer Science*, pp. 274–282, MR 1450625, doi:10.1109/SFCS.1996.548486 .

*Journal of Symbolic Logic*,

**62**(3): 708–728, MR 1472120, doi:10.2307/2275569 .

*Bulletin of the European Association for Theoretical Computer Science*(65): 66–89, MR 1650939 . Reprinted in

*Current Trends in Theoretical Computer Science*, World Scientific, 2001, MR1886033.

*Proceedings of the 30th ACM Symposium on Theory of Computing*, pp. 561–571, MR 1715604, doi:10.1145/276698.276870 .

*SIAM Journal on Computing*,

**31**(4): 1048–1075, MR 1919956, doi:10.1137/S0097539700369156 .