DD2445/FDD3445 Complexity Theory Autumn 2017
Go to the separate administrative information page to find information about instructors, prerequisites, learning outcomes, examination, and problem sets in general (with a description of the grading and peer evaluation process).
These webpages provide all documentation and information about the course, so there is no separate course memo ("kurs-PM") PDF file.
Computers are everywhere today—at work, in our cars, in our living rooms, and in our pockets—and have changed the world beyond our wildest imagination. Yet these marvellous devices are, at the core, amazingly simple and stupid: all they can do is to mechanically shuffle zeros and ones around. What is the true potential of such automated computational devices? And what are the limits of what can be done by mechanical calculations?
Complexity theory gives these deep and fascinating philosophical questions a crisp mathematical meaning. A computational problem is any task that is in principle amenable to being solved by a computer—i.e., it can be solved by mechanical application of mathematical steps. Complexity theory focuses on classifying computational problems according to their inherent difficulty, and on relating those classes of problems to each other. The goal is to understand the power of computers but also—and above all—the limitations of what problems can be solved by them, or more broadly by any type of automated computational process. A problem is regarded as inherently difficult if its solution requires unreasonably large resources regardless of which approach is used to solve it (i.e., no matter which algorithm is employed). Complexity theory formalizes this notion by introducing mathematical models of computation and quantifying the amount of resources needed to solve the problems, such as running time, memory usage, parallelism, communication, et cetera.
This course will give an introduction to computational complexity theory, survey some of the major research results, and present some of the open problems that are the focus of current research. While the intention is to give a fairly broad coverage, there will probably be a slight bias towards areas where the Theory Group at KTH has made significant contributions to the state of the art.
This course is given in periods 1-2 in the autumn of 2017. We expect to have a total of 22-23 lectures (give or take a few), with 2 lectures per week on average.
In accordance with the academic quarter tradition at KTH, 10 am in the schedule actually means 10:15 am et cetera. See the list of rooms at KTH to locate the different lecture rooms, which are mostly the seminar rooms on the 5th floor at Lindstedtsvägen 3/5. Chapter numbers in the course planning below refer to the Arora-Barak textbook.
Please note that the information below about what will be covered in future lectures is a bit tentative, since the planning might be slightly revised as we go along. The general idea behind the course is to first go over (most of) the first 9 chapters in the textbook, getting a fairly good general overview of computational complexity theory, and then spend some time on a selection of more "advanced" topics, where the textbook is followed less closely or not at all.
We will mostly be following the book
While Arora-Barak is the recommended textbook, we comment briefly on some other alternatives below. Another recent textbook on computational complexity theory is
During the second half of the course, some lectures will be partly based on research articles. A list of links to these articles will be added below later.
The intention is that the lectures will cover the material in the papers that we need, so students are not required to read these papers—the references are provided for completeness and for students interested in further reading. However, for students interested in learning more, it should be noted that many of the proofs given in class are actually not those found in the papers, and more recent survey papers of an area are likely to be better reads than the original research articles. Please do not hesitate to contact the instructor if you are interested in specific references for some specific area.
Note that if you are not at KTH, or if you are connected to the KTH
network via wireless, then you might not be able to access the PDF
files with the articles linked to below.
One way around this problem is to search for the titles of the papers
in your favourite search engine—this should hopefully help you find
free versions of the same papers on the webpages of the
authors or similar.
Another, often better, solution to this problem
is to invoke the KTH library proxy server directly in the address field of
the browser. You do this by adding
Links to the problem sets will appear as they are being posted.
Please note that the dates given below are still somewhat tentative.