1. September1999 CMSC 203 / 0201 Fall 2002 Week #14 – 25/27 November 2002 Prof. Marie desJardins clip art courtesy of www.dumpty.com

2. September1999 MON 11/25 LANGUAGES AND GRAMMARS (10.1)

3. September1999 October 1999 Concepts/Vocabulary  Formal language, syntax, semantics  Vocabulary (alphabet) V, word (sentence)  V*, language  V*  Phrase-structure grammar G=(V,T,S,P)  Alphabet V; terminal symbols T  V; nonterminal elements N=V-T; start symbol S  N; productions P: {x  y: x, y  V*}  Derivation  * (sequence of productions)  Derivation tree / parse tree  L(G): {w  T*: S  * w}

4. September1999 October 1999 Concepts/Vocabulary cont.  Types of grammars:  Type 0: no restrictions  Type 1 (context-sensitive): productions must be w 1  or w 1  w 2 where w 2 has length  w 1  Type 2 (context-free): All productions must have w 1  N (single symbol)  Type 3 (regular): All productions must have w 1  N and w 2  N or w 2 =aB where B  N  (Top-down parsing, bottom-up parsing)  (Backus-Naur form)

5. September1999 October 1999 Examples  Find a phrase-structure grammar for each of the following languages:  (a) the set of all bit strings containing an even number of 0s and no 1s  (e) the set of all strings containing more 0s than 1s  (g) the set of all strings containing an unequal number of 0s and 1s  Show a derivation tree for the string 00110010 from the grammar given in (g)

6. September1999 October 1999 Examples II  Exercise 23(a): Construct a phrase-structure grammar that generates all signed decimal numbers, consisting of a sign, either + or -; a nonnegative integer; and a decimal fraction that is either the empty string or a decimal point followed by a positive integer, where initial zeros in an integer are allowed.  Consider the 4 PSGs we’ve constructed. What type is each?

7. September1999 WED 11/27 FINITE-STATE MACHINES (10.2)

8. September1999 October 1999 Concepts/Vocabulary  Finite-state machine M=(S,I,O,f,g,s 0 ):  States S, input alphabet I, output alphabet O, transition function f: S  I  S, output function g S  I  g, initial state s 0  S  State table, state diagram  (Mealy machines, Moore machines)

9. September1999 October 1999 Examples  Vending machine model (Table 1)  Draw a state diagram for the vending machine  Draw a state diagram to recognize the signed decimal integer grammar from Exercise 23(a)  Exercise 10.3.7: Construct a FSM that delays an input string two bits, giving 00 as the first two bits of output.