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 0s followed by zero or more 1s. Let
f : B 7 B be the tot
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.e., but L is not r.e.
3 L is not r.e., but L is r.e.
4
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 Theorem 4.4.2, the number of states is n = 3.
(0)
A. Make a t
CS 4124
Solutions to Alternate Homework Assignment 10
November 17, 2005
[20] 1. Let
0
1
q0
q1
1
0, 1
1
0
q3
q2
0
be the the state diagram of the nondeterministic FSM M1 = (cfw_0, 1, Q1 , 1 , q0 , cfw_q1 ).
A. Give the function 1 as a transition table.
B.
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. The construction of the circuit depended
on a basic ci
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 combines the idea of a straight-line
program with an inst
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 language. In this problem, you will
design an NFSM M1 = cf
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 accepts a language. In this problem,
you design an FSM
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 complexity for dierent Lupanov
representations of f . Recall
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 functions from B n to B m .
Figure 1 gives a truth tab
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 (a vector in B n ) and 2n outputs (a vector in B 2 ).
Fo
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 straight-line program S to compute g .
B. Let h be the subfu
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 0s followed by zero or more 1s. Let
f : B 7 B be the tot