- Meeting 01 : Mon, Jan 11, 11:00 am-11:50 am
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Basic Admin data fixed.
Notion of Computation. A view from science and engineering sides. Algorithmic Data Processing and Mathematical Theorem proving. Ruler and Compass constructions.
- Meeting 02 : Wed, Jan 13, 09:00 am-09:50 am
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TA group allocation. Details of grading and activities of the course.
Formalizing Algorithmic Problem descriptions. Notion of an alphabet and a language.
- Meeting 03 : Thu, Jan 14, 01:00 pm-01:50 pm
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Alphabets, Strings, Operations on Strings. Languages. Operations on Languages. Powering, Asterate. Problems vs Languages.
References | : | Lecture 2 in Kozen's Textbook.
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- Meeting 04 : Mon, Jan 18, 11:00 am-11:50 am
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Modelling a push-button switch. States, Transitions. Formal definition of a finite automata. Coffee Machine example. Language accepted by the FA.
- Meeting 05 : Tue, Jan 19, 10:00 pm-10:50 pm
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A mathematical proof that design of the push button switch indeed meets the user requirements. More examples of design and proof of correctness of finite automata.
References | : | The second example is from Lecture 3 in [K]
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Exercises | : | Generalize the construction and proof to show that the following set S(p,k) can be accepted by a finite automaton. S(p,k) is the set of strings over the alphabet {0,1,2 ... p-1} which are p-ary representations of multiples of k (leading 0s are allowed). How many states does your automaton use?
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- Meeting 06 : Wed, Jan 20, 09:00 am-09:50 am
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Regular languages. Are all languages regular? Closure properties of the set of regular languages. Complementation. Product construction.
References | : | Lecture 3 in [K]
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- Meeting 07 : Wed, Jan 27, 09:00 am-09:50 am
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Limitations of Finite automaton. Two example languages which cannot be accepted by finite automaton. Proof that they are not regular - demonstrations of how formally exploit the "finiteness" of the number of states.
- Meeting 08 : Thu, Jan 28, 01:00 pm-01:50 pm
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More examples of non-regularity. Abstraction from the proofs to a formal statement of pumping Lemma. View of the Game with the Demon.
- Meeting 09 : Mon, Feb 01, 11:00 am-11:50 am
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Proof of the pumping Lemma. Applications.
- Meeting 10 : Tue, Feb 02, 10:00 pm-10:50 pm
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More example applications of the pumping lemma. Strengthened versions of the pumping lemma.
- Meeting 11 : Wed, Feb 03, 09:00 am-09:50 am
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Collapsing states in a finite automaton. Minimization.
- Meeting 12 : Thu, Feb 04, 01:00 pm-01:50 pm
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Quotient construction and its correctness.
Marking Algorithm and its correctness.
- Meeting 13 : Thu, Feb 04, 02:00 pm-02:50 pm
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Viewing automaton as a string classifier. Myhill-Nerode relations. From Automata to Myhill-Nerode relations. Using Myhill-Nerode theorem to show non-regularity.
- Meeting 14 : Mon, Feb 08, 11:00 am-11:50 am
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More examples of using Myhill-Nerode theorem to show non-regularity. From Myhill-Nerode relations to Automaton. Using Myhill-Nerode theorem to show optimality of automaton.
- Meeting 15 : Tue, Feb 09, 10:00 pm-10:50 pm
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Coarsest and Finest Myhill-Neorde Relations with respect to the same language. A characterization for the coarsest Myhill-Nerode relation. Connections to Minimal Automata.
- Meeting 16 : Thu, Feb 11, 01:00 pm-01:50 pm
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The Two-way Finite Automaton (2way FAs). An example language where 2-way FA design is easier. The formal model of computation. Accepting, Rejecting and Looping.
- Meeting 17 : Mon, Feb 15, 11:00 am-11:50 am
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Proof that 2-way finite automaton accepts only regular languages. A nontrivial use of Myhill-Nerode theorem.
- Meeting 18 : Tue, Feb 16, 10:00 pm-10:50 pm
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Non-deterministic automaton, motivation, formal definition, examples, and the view as a subset automaton.
- Meeting 19 : Wed, Feb 17, 09:00 am-09:50 am
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Formal proof of the subset construction. A "guess+verify view" of non-determinism. Epsilon-transitions and applying subset construction in that case.
- Meeting 20 : Wed, Feb 24, 09:00 am-09:50 am
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TBA
- Meeting 21 : Thu, Feb 25, 01:00 pm-01:50 pm
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Expressing languages using expressions.
- Meeting 22 : Mon, Feb 29, 11:00 am-11:50 am
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From Finite Automaton to Regular Expressions. Minimal set of operations for regular expressions.
- Meeting 23 : Tue, Mar 01, 10:00 pm-10:50 pm
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Closure of Regular Languages under Homomorphisms and image of homomorphisms. The Hamming Distance Language is regular for a fixed distance case.