CS 4124
Solutions to Homework Assignment 1
August 30, 2005
[20] 1. B = cfw_0, 1 is the binary alphabet. Let L = cfw_0 cfw_1 be the language over B
containing all strings that consist of zero or more 0
CS 4124
Solutions to Homework Assignment 12
December 6, 2005
[20] 1. Let be an alphabet and L a language over . Then L satises exactly one of the
following four properties:
1 L is decidable.
2 L is r.
CS 4124
Solutions to Homework Assignment 11
November 29, 2005
[20] 1. The state diagram of DFSM M1 = (cfw_0, 1, cfw_q1 , q2 , q3 , 1 , q1 , cfw_q2 , q3 ) is given in
Figure 1. In the context of Theore
CS 4124
Solutions to Homework Assignment 9
November 8, 2005
[20] 1. In class, we discussed how a logic circuit can be built to simulate the computation
of a Turing machine M on an input x for T steps.
CS 4124
Solutions to Homework Assignment 8
October 26, 2005
[20] 1. Simple Stack Machine. This problem is about a very simple model of computation, called the simple stack machine (SSM) model, that co
CS 4124
Solutions to Homework Assignment 7
October 18, 2005
[20] 1. As dened in class, a nondeterministic nite state machine (NFSM) is a model
of computation that is a six-tuple and that accepts a lan
CS 4124
Solutions to Homework Assignment 6
October 11, 2005
[20] 1. As dened in class and in Section 3.1, a deterministic nite state machine (FSM) is
a seven-tuple. An FSM computes a function and also
CS 4124
Solutions to Homework Assignment 5
September 27, 2005
[20] 1. In this problem, the number of inputs to an arbitrary function f : B n B
is n = 210 = 1024. You are to estimate the circuit comple
CS 4124
Solutions to Homework Assignment 4
September 20, 2005
[20] 1. In this problem, all circuits are to use the standard basis 0 = cfw_, , .
A. Denition 2.11.1 denes Sn,m to be the set of symmetric
CS 4124
Solutions to Homework Assignment 3
September 14, 2005
[20] 1. Figure 2.12 in the textbook illustrates the recursive construction of an n-bit decoder,
n
which is a logic circuit with n inputs (
CS 4124
Solutions to Homework Assignment 2
September 6, 2005
[20] 1. Let g : B 4 B 3 be given by this equation:
g (w, x, y, z ) = (w x) (y z ), (w x) (w z ), (y x) (w z ).
A. Construct a compact strai
CS 4124
Solutions to Homework Assignment 1
August 30, 2005
[20] 1. B = cfw_0, 1 is the binary alphabet. Let L = cfw_0 cfw_1 be the language over B
containing all strings that consist of zero or more 0