Lecture Notes 11: Perspectives on REs and FAs; and Properties of Regular Languages

Outline

This class we'll discuss:

• Perspectives on simple machines
• Properties of Regular Languages
• Looking ahead: Context-Free Grammars
• CFG examples

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Some Perspective

Why are we asking you all of these questions about regularity of languages, etc.?

REs and FAs are really simple computational machines.

What does this have to do with getting your Java code to compile, or using dynamic programming, or ...

Turns out that there are some surprisingly algorithmic things we can do when we start asking questions about these simple machines.

Let’s take a look at some questions we might ask.

Why are these questions important?

(Wait; then Click)

It's not about simply building a machine that might do something,
It's about knowing, before expending unnecessary effort if:

1. we are reinventing the wheel.
2. we are building something that never terminates
3. we are building something that works but is extremely inefficient
4. etc

In Real Life

1. Do we have a way of answering these questions about our own programs?
2. In a way, all programs do symbol processing
3. In a way all of them are like little Machines
4. If we can represent processes as FAs or REs, we can answer the questions shown above

Activity 4 [5 minutes]:

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Intro: Context-Free Grammar

EQ, HALF, PAL







Finite automata and regular expressions are limited

They both only match patterns that can be described by reaching L to R

Some patterns are more interesting…







Seems like PAL lives really close to Regular: there’s a structure to the words that’s ALMOST regular… but the pattern is in the middle.



S ->g N_phrase V_phrase



N -> article noun

V -> conjugated verb

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Next class: Context-Free Grammars

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Homework

[Due for everyone]

Problem Set 03: Due 10/18 at 5 PM

[Optional]

TODO