outl
ine
- Mathematical Sophistication.
We'll develop the syntax and semantics of a simple Boolean logic
while reviewing (or perhaps, introducing) the following
mathematical concepts:
- sets and sequences and graphs
- functions (mappings)
- relations and alphabets and languages
- proof techniques
- Finite Automata.
We will investigate the power (and
limitations) of computation with a small, finite amount of
memory.
- Deterministic Finite Automata (DFAs)
- state diagrams
- precise definition
- regular languages (as problems)
- acceptance and rejecion of strings (algorithms)
- Non-Determinism
- Non-deterministic Finite Automata (NFAs)
- equivalence in computing power of NFAs and DFAs
- Regular Expressions
- definitions
- equivalence in descriptive power of regular expressions and DFAs
- Non-regular languages
- Pumping Lemma for regular languages
- state minimization (via the Myhill-Nerode Theorem)
- examples of non-regular languages which may be pumped
- Context-Free Languages.
- Context-Free Grammars
- Nondeterministic Push Down Automata
- Equivalience of PDAs and CFGs
- Turing Machines.
- Decidability.
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