[syllabus] | [lecture notes] | [HW1-6,Q1] | [HW7-10,Q2,F] | [project]
[simulators/parsers] | [language definitions] | [automata definitions] | [computable definitions]
The most important item on all homework is YOUR submit
Homework must be submitted when due. You loose 10%, one grade, the first day homework is late. Then 10% more per week, each week homework is late. Max of 50% off. A ZERO really hurts your final points. Do and turn in all homework, even if it is late. See HW1 for submit details. (no late penalty for online courses)
Open book, open note. Multiple choice questions based on lectures, and homework. No cheating = no discussions with other students. Exam covers lectures: 12 -18 Exam covers homework: HW4, HW5 and HW6 Get exam, edit answers, save, submit. cp /afs/umbc.edu/users/s/q/squire/pub/download/cs451q2.doc . # your directory libreoffice cs451q2.doc or scp, winscp, to windows and use Microsoft word submit cs451 q2 cs451q2.doc
1) Construct a NPDA equivalent to the following grammar:
G = ( {S, A}, {a, b}, P, S )
Productions
S -> a A A
A -> a S | b S | a
Define all the components M = ( Q, Sigma, Gamma, delta, q0, Z0, F)
Show your work, partial credit given
2) Construct a grammar equivalent to the following PDA
M = ({q0, q1}, {0,1}, {Z0, X}, delta, q0, Z0, phi)
delta Sigma input, Gamma Top of stack
| 0,Z0 | 0,X | 1,Z0 | 1,X | eps,Z0 | eps,X
----+-----------+----------+------------+------------+------------+--
q0 | phi | {(q1,X)} | {(q0,XZ0)} | {(q0,XX)} | {(q0,eps)} | phi
q1 | {(q0,Z0)} | phi | phi | {(q1,eps)} | phi | phi
eps is short for epsilon the null string.
Define all components G = ( V, T, P, S)
Show your work, partial credit given
submit cs451 hw7 your.file
You are allowed to use the executable 'cykp' and copy the V table.
You are allowed to look at C++ code in cykp.cpp, cykp.java, cykp.py
you may use hw8.g or if problem with my code, g_83.g
1) Given the CFG G = ( {S, A, B, C}, {a, b}, P, S
with Productions
S -> AB | BC
A -> BA | a
B -> CC | b
C -> AB | a
Determine if these strings are in the language:
a) aaaaa
b) aaaaaa
c) baabab
You must show the V table.
Hint: use hw8.g and any cykp.
cyk_hw8.out
or use g_83.g and any cykp.
cyk_g_83.out
2) Let G be a CFG in Chomsky Normal Form
Give an algorithm to determine the number of distinct
derivations of a string x from ( a) or b) or c) above).
You can give the list of productions used or the tree
of variables for the algorithm.
You may show neat pseudo code with comments
You have complete freedom on how to proceed.
One method is to assume the two-tuples from lecture 24
are in the sets in the V matrix. Systematically walk
the indexes and keep a count of successful walks.
submit cs451 hw8 your.file
1) write out the steps using the pumping lemma for CFL's to prove that
i i i
L = { a b c | i >= 1 } is not a CFL.
2) Using the steps in 1) [go back and add more if you missed some],
prove, using the pumping lemma for CFL's that
i j k
L = { a b c | i < j < k } is not a CFL.
submit cs451 hw9 your.file
1) Write the machine description for a Turing machine, including
delta transition table for the specific machine that
starts with a number n on the tape and finishes with
n squared on the tape. n on the input is just n zeros followed
by blank tape. tape 000#b
P.S. 3 squared is nine 000000000#b
Hint: copy the input string as many times as there are 0's
on the tape at the start. 000#b000000000#b
(ok to leave initial tape with #b followed by copies)
Code your program and test it using the Turing Machine simulator,
"tm" The name of your program is to be 'square.tm'
More details are found in Simulators.
tm < square.tm > square_tm.out # best my code should be working
python3 tm.py square.tm > square_tm_py.out # my code may have bugs
java tm square.tm > square_tm_java.out # my code may have bugs
Submit your homework on gl using submit cs451 hw10 square.tm
submit cs451 hw10 your.file
I suggest 4 input tapes:
You get 10 points if 1#b has final tape 1
you get 15 points if 11#b has final tape 1111
you get 20 points if 111#b has final tape 111111111
you get 25 points if 1111#b has final tape 1111111111111111
Sample .tm files and results cpp tm java tm trace all for debugging
tm < add.tm > add_tm.out # tm.cpp download just tm
add.tm with trace all
add_tm.out with trace all
tm < add_nt.tm > add_nt_tm.out
add_nt.tm no trace all
add_nt_tm.out no trace all
tm < l0n1na.tm > l0n1na_tm.out
l0n1na.tm with trace all
l0n1na_tm.aout with trace all
tm < l0n1n.tm > l0n1n_tm.out
l0n1n.tm no trace all
l0n1n_tm.out no trace all
java tm add.tm > add_tm_java.out # tm.java download and compile tm.java
add.tm with trace all
add_tm_java.out with trace all
java tm add_nt.tm > add_nt_tm_java.out
add_nt.tm no trace all
add_nt_tm_java.out no trace all
java tm l0n1na.tm > l0n1na_tm_java.out
l0n1na.tm with trace all
l0n1na_tm_java.out with trace all
java tm l0n1n.tm > l0n1n_tm_java.out
l0n1n.tm no trace all
l0n1n_tm_java.out no trace all
For more example of programming a Turing Machine see Turing Machine simulator
Really big .tm for general binary number addition b_add.tm
Open book, Open note. Covers all lectures, all homework
and project. Multiple choice and short answer questions.
No cheating = no discussion with other students.
1) go over the Quiz 1 and Quiz 2
the final exam will include some of these questions
2) You may find it helpful to go over the
Lecture Notes but not the details of constructions
3) Understand what classes of languages go with what machines,
automata and Turing machines,
and grammars and regular expressions
4) Understand the statement of the Pumping Lemma for Context Free Languages
5) Understand the Halting Problem and why it is not computable
6) Understand the Church Turing Hypothesis
Get .doc, edit, save, exit, submit:
cp /afs/umbc.edu/users/s/q/squire/pub/download/cs451fin.doc . # your directory
libreoffice cs451fin.doc
submit cs451 final cs451fin.doc
last updated 5/6/2021