Comp. Sci. 741

Computational Complexity

Spring, 2003



Student Presentations:
May 9: Audrey Lee; George Bissias (Note: Friday not Wednesday class next week)
May 12: Kazu Hirata; Matt Yurkewych
May 14: Martin Allen; Ross Fairgrieve
Projects: The following are a few papers that might interest you as you are
deciding what to do your projects on. Dave and I will add a few others over the next
few weeks and suggestions and comments are welcome!

Micah Adler and Neil Immerman,
An n! Lower
Bound On Formula Size, to appear in ACM Transactions on Computational
Logic. Preliminary version appeared in LICS '01, 197206.
 Martin Grohe and Markus Frick, "The complexity of firstorder and monadic
secondorder logic revisited," . Conference version appeared in Proceedings of the
17th IEEE Symposium on Logic in Computer Science (LICS'02), pp. 215224, [I mentioned
this paper for its beautiful lower bounds on the constants for problems in parameterized complexity.]

M. Grohe and T. Schwentick, ``Locality of
orderinvariant firstorder forumlas, MFCS'98, 437445. Full version to
appear in ACM TOCL. [This one has been tentatively chosen by Ross Fairgrieve.]

Guozhu Dong, Leonid Libkin, and Limsoon Wong, "Incremental recomputatin in local
languages," Information and Computation 181(2) (2003), 8897.
 Leonid Libkin, Limsoon Wong, "On the power of aggregation in relational query
languages," (1997), Proccedings of the Database Programming Languages, LNCS vol. 1369,
Springer, 260280. [This one has been chosen by Matt Yurkewych.]

J.Hastad, R.Impagliazzo, L. Levin, M. Luby, "A Pesudorandom Generator from any
Oneway Function SICOMP 28(4) 13641396 (1999)
 [Beame, Impagliazzo, Pitassi] showed "Improved Depth Lower Bounds for Small Distance
Connectivity" (journal version: Computational
Complexity vol 7, #4, 1998, p. 325) that polysize circuits
need depth log log log n, in order to follow a path of length log n
in a graph of size n. [This one has been chosen by Audrey Lee.]

A. Yao, "Classical Physics and the ChurchTuring Thesis," to appear in JACM, Jan. 03.
HW1, due Wed., 2/12: please do the following exercises from Descriptive
Complexity: 1.5, 1.7, 1.8, 1.12, 1.13, and 1.23.
HW2, due Fri, 3/14: please do the following exercises from Descriptive
Complexity: 1.31, 2.3, 2.8: [this is the famous space hierarchy theorem. I
suggest that you read a proof and understand it well, and then write it up in your
own words. You should still of course cite your sources], 2.16, 2.17, 3.4, 3.7.
Meeting Times: MW 10:35  11:50, CMPS 140. Note: This time may conflict
with some faculty candidate talks. Please keep the same time slot open on Fridays,
because when there is a faculty candidate talk on a Monday or Wednesday during class time,
we will usually switch that class to Friday so as not to conflict with the
candidate's talk. All graduate students are strongly encouraged to come to all
faculty candidate talks!
Instructors: David Mix
Barrington and Neil Immerman
CMPSCI 741: Office Hours, Fall 2002 
Neil Immerman, CompSci Bldg 374,
immerman@cs.umass.edu  Tues, Wed: 2:30  3:30, and by appointment.

David Mix Barrington, CMPSCI 210  Tues, 9:00  11:30 
What this course is about: This is an advance course/seminar in complexity
theory. This course is typically taught every other year, and the topics can vary.
For spring, 2003, we are planning to concentrate on descriptive complexity, but to
include other topics and recent advances in complexity theory.
Descriptive complexity is an approach, based on mathematical logic, to
classifying the relative difficulty of computational problems (particularly
queries to a database). While traditional complexity theory concentrates
on the resources needed to compute the answer to a query, descriptive
complexity focuses on the resources needed to describe the query in
some logical formalism  how many variables, how many quantifiers, which
forms of induction, and so forth. Surprisingly, computational complexity
classes like P and NP have natural characterizations in descriptive
complexity, as do all other wellstudied complexity classes.
In this course, among other things, we will:
 Describe the logical formalism used for queries and its various
resource measures,
 Prove characterizations of several important computational complexity
classes in terms of descriptive complexity,
 Use pebble games to prove upper and lower bounds on the descriptive
complexity of some important queries, and
 Examine extensions to the model, such as dynamic complexity ,
which measures the descriptive complexity of processing updates and
queries to a database.
 The applications that we investigate will depend on the interests of
those who attend.
Text: Descriptive Complexity, by Neil Immerman, Springer Graduate
Texts in Computer Science, 1999. This will be available at the Jeffrey Amherst
College Store in downtown Amherst.
Prerequisite: CMPSCI 601 or permission of at least one of the instructors.