CMPSCI 601: Theory of Computation

David Mix Barrington

Spring, 2003

Homework Assignment #1

Due Monday 1 March 2004 in class

(Wed 10 March 2:00 pm EST for off-campus students)

Most of the problems are from [BE] and are to be submitted to the Grade Grinder if they are marked for electronic submission. The last two are written here. Question 3 was replaced on 21 February 2004.

• Question 1 (80): Do the following problems in [BE]: 3.3, 3.15, 3.21, 4.24, 6.2, 6.14, 6.32, 8.4, 8.46. 8.42 (10), 17.4, 17.13 (10), 17.16 (10). The problems not marked "(10)" are five points each.

• Question 2 (10): Describe a one-tape Turing machine that when started on input "w", a string in {0,1}^*, halts with "ww" on the tape. You may define the tape alphabet as needed, and omit transitions that will not be used in a successful computation.

• Question 3 (10+10): (Question modified Sat 21 Feb 2004) Explain informally why the function Times (which inputs two $n$-bit binary strings interpreted as numbers x and y, and outputs their product xy) is in the class F(DTIME(n²)). For up to ten points extra credit, explain informally why Times is in the class is in the class F(DSPACE(log n)). Recall that the definition of the latter class refers to a Turing machine with a read-only input tape, one or more read/write work tapes, and a write-only output tape.

Last modified 4 March 2004