This page contains as a list of the material actually covered so far CS 457 for Spring 2006, as well as an outlook on the upcomming lecture(s). Note that the planned coverage for upcomming lectures might change.
Here is a shortcut the most recent lecture and one to the next lecture.
Material Covered So Far
- Lecture 0 (Monday, 1/30/06)
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Introduction, Course Fomalities,
Example of problem that is not computable
Research Topic: none - Lecture 1 (Wednesday, 2/1/06)
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This class will be held in the lab
(Room 206, classroom building)
Introduction to Finite State Machines using JFLAP .
Research Topics:-
Historical Background:
- Alan Turing ("Turing Machine", "Church-Turing thesis")
- Alonzo Church ("Church-Turing thesis")
- Emil Post ("Post Machine", "Post's Correspondance Problem")
- Noam Chomsky ("Chomsky Hierarchy")
- Kurt Gödel ("Undecidability", "Incompleteness Theorem")
- Finite State Machines
- Design one homework problem on Finite State Machines for the rest of the class.
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Historical Background:
- Lecture 2 (Wednesday, 2/8/06)
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Discussion of research results.
Properties of finite state machines, Regular Languages,
Mathematical background: sets, languages, strings,
Example to motivate construction of product automaton
Research Topics:- Construction of a product automaton: given two finite state machine M1 and M2, build a machine that accepts all strings that are accepted by both (alternatively: either one) M1 and (or) M2
- Lecture 3 (Wednesday, 2/15/06)
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Discussion of research results:
Review of construction of product automaton
Examples to motivate nondeterministic finite state machines
Research Topics:-
Nondeterminism, nondeterministic machines.
The Sipser book (on reserve in the library) has a pretty good explanaiton of this topic.
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Nondeterminism, nondeterministic machines.
- Lecture 4 (Wednesday, 3/21/06)
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Discussion of research results: Non deterministic machine.
Comparisson of non-deterministic and deterministic machines, examples
Conversion of non-deterministic to deterministic machines.
Research Topics: to be announced - Lecture 5 (Wednesday, 3/1/06)
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Discussion of research results: Conversion from deterministic to
nondeterministic machines
NFAs with ε transitions, NFA for union of two regular sets
Regular operations
Research Topics: How can one use ε-NFAs to build recognize the concatenation of two regular sets, and the "repitition" (*) of a regular set ? - Lecture 7 (Wednesday, 3/8/06)
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Discussion of research results: Closure of Regular sets under
regular expression
Regular expressions
Research Topics:- Find examples for languages that are not regular.
- Why are these sets not regular?
- Lecture 8 (Wednesday, 3/15/06)
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Class was cancelled
Research Topics: to be announced - Lecture 9 (Wednesday, 3/22/06)
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Converting a DFA into a Regular Expression
Research Topics: to be announced - Lecture 10 (Wednesday, 3/29/06)
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Non-regular languages, Pumping Lemma
Research Topics: to be announced - Lecture 11 (Wednesday, 4/5/06)
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More examples on the Pumping Lemma
Research Topics: To be announced
