CS453 Lecture Regular Expressions and Transition Diagrams 2

Should be done

 Lab hours and Office hours

 Sign up for the mailing list at , starting to send important info to list – http://groups.google.com/group/cs453-spring-2011

 Read Ch 1 and skim Ch 2 through 2.6, read 3.3 and 3.4

 Start working with the MiniSVG start up code – You should at least step through the existing code with a debugger before Thursday’s class

CS453 Lecture Regular Expressions and Transition Diagrams 3

Do Soon

Quiz 1 is due tonight, was posted Tuesday night

Continue working with the MiniSVG start up code – You should at least step through the existing code with a debugger before Thursday’s class

 Send email to mstrout@cs.colostate.edu if you would like to help put together Meggy Jr devices this Sunday

– 2-3pm in rm 425 – Will only be able to accommodate the first 8 students, still 3 slots left – Will open it up for grad students and other undergrads on Thursday – We will have one other session sometime next week Tuesday or Thursday night

 HW1 due Wednesday

CS453 Lecture Regular Expressions and Transition Diagrams 4

Plan for Today

Interpreter and Compiler Structure, or Software Architecture

 Overview of Programming Assignments –  The MiniSVG interpreter and MeggyJava compiler we will be building.

CS453 Lecture Regular Expressions and Transition Diagrams 5

Structure of a Typical Compiler

“sentences”

Synthesis

optimization

code generation

target language

IR

IR code generation

IR

Analysis

character stream

lexical analysis

“words” tokens

semantic analysis

syntactic analysis

AST

annotated AST

interpreter

CS453 Lecture Regular Expressions and Transition Diagrams 6

Example MeggyJava program

import meggy.Meggy;

class PA3Flower {public static void main(String[] whatever){{

  // Upper left petal, clockwise   Meggy.setPixel( (byte)2, (byte)4, Meggy.Color.VIOLET );   Meggy.setPixel( (byte)2, (byte)1, Meggy.Color.VIOLET);   …   }}

CS453 Lecture Regular Expressions and Transition Diagrams 7

Atmel assembly for Meggy.setPixel() call …main:… call _Z18MeggyJrSimpleSetupv # Push constant 2 onto stack ldi r24, 2 push r24 # Push constant 4 onto stack ldi r24, 4 push r24 # Push Meggy.Color.VIOLET onto the stack. ldi r22, 6 push r22 # Pop the arguments into registers in reverse order. pop r20 pop r22 pop r24 call _Z6DrawPxhhh call _Z12DisplaySlatev

CS453 Lecture Regular Expressions and Transition Diagrams 8

Structure of the MeggyJava Compiler

“sentences”

Synthesis Analysis

character stream

lexical analysis

“words” tokens

semantic analysis

syntactic analysis

AST

AST and symbol table

code gen

Atmel assembly code

PA2: MeggyJava and Atmel warmup PA3: setPixel compiler PA4: add control flow PA5: add functions PA6: add variables and objects PA7: add arrays

CS453 Lecture Regular Expressions and Transition Diagrams 9

Structure of the MiniSVG Interpreter (PA1)

calls to report and draw routines

Analysis

character stream

lexical analysis

tokens

syntactic analysis

Rectangle: (0,0) 500x500 color: GREEN Circle: (120,150) radius:60 color: WHITE Circle: (350,150) radius:60 color: WHITE Circle: (120,150) radius:30 color: BLUE Circle: (350,150) radius:30 color: BLUE Circle: (120,150) radius:10 color: BLACK Circle: (350,150) radius:10 color: BLACK Circle: (250,300) radius:100 color: RED Line: (250,350) (350,350) color: BLACK Line: (0,100) (100,100) color: BLACK Line: (100,200) (200,200) color: BLACK Line: (300,400) (400,400) color: BLACK Line: (500,500) (500,500) color: BLACK Line: (50,100) (100,100) color: BLACK Line: (150,200) (200,200) color: BLACK Line: (200,400) (400,400) color: BLACK Line: (400,200) (400,200) color: BLACK Line: (450,200) (400,200) color: BLACK

CS453 Lecture Regular Expressions and Transition Diagrams 10

face.svg

  <svg xmlns="http://www.w3.org/2000/svg">  <!-- THIS MAKES A FACE!!! -->  <!-- From Stephanie and Kiley -->   <!-- background -->   <rect x = "0" y = "0" width = "500" height = "500" fill="green" />

  <!-- eyes -->   <circle cx="120" cy="150" r="60" fill="white" />   ...

  <!-- mouth -->   <circle cx="250" cy="300" r="100" fill="red" />   <line x1="250" y1="350" x2="350" y2="350" stroke="black" />

  <!-- hair -->   ...  </svg>

CS453 Lecture Regular Expressions and Transition Diagrams 11

MiniSVG Renderer

<svg xmlns="http://www.w3.org/2000/svg">

<!-- rectangles --> <rect x="20" y=" 20" width="300" height="250" fill="red" /> <rect x="30" y="20" width="300" height="250" fill="blue" /> <rect x = "40" y = "20" width = "300" height = "250" fill="green" />

<!-- white circle on top of rectangles --> <circle cx="120" cy="150" r="60" fill="white" />

<!-- black diagonal line --> <line x1="0" y1="0" x2="300" y2="300" stroke="black" />

</svg>

About The Slides on Languages and Finite Automata

  Slides Originally Developed by Prof. Costas Busch (2004) –  Many thanks to Prof. Busch for developing the original slide set.

  Adapted with permission by Prof. Dan Massey (Spring 2007) –  Subsequent modifications, many thanks to Prof. Massey for CS 301 slides

  Adapted with permission by Prof. Michelle Strout (Spring 2011) –  Adapted for use in CS 453

  A language is a set of strings

  String: A finite sequence of letters

Examples: “cat”, “dog”, “house”, …

Defined over a fixed alphabet:

{ }zcba ,,,, …=!

Languages

Empty String

  A string with no letters:

  Observations:

!

"

!

" = 0

"w = w" = w

"abba = abba" = abba

Regular Expressions

  Regular expressions describe regular languages

  Example:

describes the language

!

(a | (b)(c)) *

!

L((a | (b)(c))*) = ",a,bc,aa,abc,bca,...{ }

Recursive Definition for Specifying Regular Expressions

!

", #, $

!

r1 | r2(r1)(r2)r1 *

r1( )

Are regular expressions

Primitive regular expressions:

2r1rGiven regular expressions and

Example Regular Expressions and Regular Definitions

Keywords

Operations

Identifiers

Numbers

CS453 Lecture Regular Expressions and Transition Diagrams 17

Finite Automaton

Input

String Output

String

Finite Automaton

Finite Accepter

Input

“Accept” or “Reject”

String

Finite Automaton

Output

Transition Graph

initial state

final state “accept” state

transition

Abba -Finite Accepter

0q 1q 2q 3q 4qa b b a

5q

a a bb

ba,

ba,

Initial Configuration

1q 2q 3q 4qa b b a

5q

a a bb

ba,

Input String a b b a

ba,

0q

Reading the Input

0q 1q 2q 3q 4qa b b a

5q

a a bb

ba,

a b b a

ba,

0q 1q 2q 3q 4qa b b a

5q

a a bb

ba,

a b b a

ba,

0q 1q 2q 3q 4qa b b a

5q

a a bb

ba,

a b b a

ba,

0q 1q 2q 3q 4qa b b a

5q

a a bb

ba,

a b b a

ba,

0q 1q 2q 3q 4qa b b a

Output: “accept”

5q

a a bb

ba,

a b b a

ba,

Input finished String Rejection

1q 2q 3q 4qa b b a

5q

a a bb

ba,

a b a

ba,

0q

0q 1q 2q 3q 4qa b b a

5q

a a bb

ba,

a b a

ba,

0q 1q 2q 3q 4qa b b a

5q

a a bb

ba,

a b a

ba,

0q 1q 2q 3q 4qa b b a

5q

a a bb

ba,

a b a

ba,

0q 1q 2q 3q 4qa b b a

5q

a a bb

ba,Output: “reject”

a b a

ba,

Input finished

The Empty String

1q 2q 3q 4qa b b a

5q

a a bb

ba,

ba,

0q

!

"

1q 2q 3q 4qa b b a

5q

a a bb

ba,

ba,

0q

Output: “reject”

Would it be possible to accept the empty string?

!

"

Another Example

a

b ba,

ba,

0q 1q 2q

a ba

a

b ba,

ba,

0q 1q 2q

a ba

a

b ba,

ba,

0q 1q 2q

a ba

a

b ba,

ba,

0q 1q 2q

a ba

a

b ba,

ba,

0q 1q 2q

a ba

Output: “accept”

Input finished Rejection

a

b ba,

ba,

0q 1q 2q

ab b

a

b ba,

ba,

0q 1q 2q

ab b

a

b ba,

ba,

0q 1q 2q

ab b

a

b ba,

ba,

0q 1q 2q

ab b

a

b ba,

ba,

0q 1q 2q

ab b

Output: “reject”

Input finished

Which strings are accepted?

Formalities

  Deterministic Finite Accepter (DFA)

( )FqQM ,,,, 0!"=

Q!

!

0q

F

: set of states

: input alphabet

: transition function

: initial state

: set of final states

Input Alphabet !

0q 1q 2q 3q 4qa b b a

5q

a a bb

ba,

{ }ba,=!

ba,

Set of States Q

0q 1q 2q 3q 4qa b b a

5q

a a bb

ba,

{ }543210 ,,,,, qqqqqqQ =

ba,

Initial State 0q

1q 2q 3q 4qa b b a

5q

a a bb

ba,

ba,

0q

Set of Final States F

0q 1q 2q 3qa b b a

5q

a a bb

ba,

{ }4qF =

ba,

4q

Transition Function !

0q 1q 2q 3q 4qa b b a

5q

a a bb

ba,

QQ !"#:$

ba,

( ) 10, qaq =!

2q 3q 4qa b b a

5q

a a bb

ba,

ba,

0q 1q

( ) 50, qbq =!

1q 2q 3q 4qa b b a

5q

a a bb

ba,

ba,

0q

0q 1q 2q 3q 4qa b b a

5q

a a bb

ba,

ba,

( ) 32, qbq =!

Transition Function !

0q 1q 2q 3q 4qa b b a

5q

a a bb

ba,

! a b0q

1q

2q

3q

4q

5q

1q 5q

5q 2q5q 3q

4q 5q

ba,5q5q5q5q

CS453 Lecture Regular Expressions and Transition Diagrams 54

Transition Diagrams

Definition - A finite automata specialized for lexical analysis

Differences from finite state automata - Finding more than one string in a single input stream

- Do not accept until hit a character with no out transition - Asterisk notation indicates the need to put last character back in input

- Do not show sink states

0q 1q 2q 3q 4qa b b a

Initial Configuration

Input String a b b a

0q

a a a a

1q 2q 3q 4qa b b a

b b $ b b

0q 1q 2q 3q 4qa b b a

a b b a a a a ab b $ b b

Recognize token abba when attempt to process 3rd a

token

a b b a a a a ab b $ b b

0q 1q 2q 3q 4qa b b a

a b b a a a a ab b $ b b

1q 2q 3q 4qa b b a0q

token token token

a b b a a a a ab b $ b b

0q 1q 2q 3q 4qa b b a

!

q5 *ws

a b b a a a a ab b $ b b

0q 1q 2q 3q 4qa b b a

!

q5 *ws

token

a b b a a a a ab b $ b b

1q 2q 3q 4qa b b a

!

q5 *ws

0q

a b b a a a a ab b $ b b

1q 2q 3q 4qa b b a0q

token

!

q5 *ws

CS453 Lecture Lexical Analysis with JLex 63

Demonstration of Longest Match and Priority