LING 388: Language and Computers

LING 388: Language and Computers Sandiway Fong Lecture 8: 9/20

Administrivia • LING 388 Homework #2 • handed out today • submit homework by email • sandiway@email.arizona.edu • due date is one week from now • Monday September 27th (by midnight) • Next time • Back in classroom

SWI-Prolog Cheatsheet • How to start it? • from the Windows Program menu • How to see what’s in the database? • ?- listing. • How to see what the current working directory is? • ?- working_directory(X,Y). • X: current working directory, Y: new working directory • How to change to a new working directory? • ?- working_directory(X,NEW). • How to turn on tracing mode for the Prolog debugger? • ?- trace. • How to turn off Prolog debugger? • ?- nodebug. • How to see non-abbreviated results? (…) • ?- set_prolog_flag(toplevel_print_options,[max_depth(0)]).

a s x a b y b Exercise 1: FSA L = {a+b+}

Exercise 1: FSA • FSA machine for L = {a+b+} • state s: • s([a|L]) :- x(L). match input string beginning with a and call state x with remainder of input • State x: • x([a|L]) :- x(L). • x([b|L]) :- y(L). • state y: • y([]). % end state • y([b|L]) :- y(L). • Enter this machine into the database and trace machine on queries: • ?-s([a,a,b,b]). Yes • ?- s([a,b,a]). No • ?- s([a,X]). X = b

Exercise 1: FSA • Homework Question (A): (2pts) • What and how many answers does the query ?- s([X,Y,Z]). return? • Homework Question (B): (2pts) • If the rule x([a|L]) :- x(L). is removed from the program, what language does the revised FSA accept?

s b w a x a b y a ! z Exercise 2: FSA • Homework Question 2 (4pts) • Implement the FSA shown below for Sheeptalk (baa! baaa! baaaa! …) • Show the machine accepts strings • baa! baaaa! • Show the machine rejects strings • ba! baa baba! • Submit both the program • and your output

Exercise 3: Regular Grammars • A regular grammar for the man I saw: • dp --> [the], np. • np --> [man], relc. • relc --> [that], sorel. • sorel --> [i], vporel. % object relative sentence • vporel --> [saw]. • Verify rules work using query: • ?- dp([the,man,that,i,saw],[]). Yes • Add regular grammar rules to handle • the man that you saw • the man that you met

Exercise 3: Regular Grammars • Homework Question A (4pts) • Modify regular grammar to accept recursive embeddings of the form • the man that I saw that you heard • the man that you heard that I saw • Submit both your grammar and the output • Note: make sure your grammar is still regular • Hint: it may be useful to draw the equivalent FSA

Exercise 3: Regular Grammars • Homework Question B (2pts) • Modify regular grammar to allow the option of dropping the relative pronoun that, e.g. • the man that I saw • the man I saw • Submit both your grammar and the output • Note: make sure your grammar is still regular

A a B b Exercise 4: Beyond Regular Grammars • In Lecture 7, we mentioned • anbn is not a regular language • And that a grammar with both left and right recursive rules can accept it • a --> [a], b. • b --> [b]. • b --> a, [b]. • Verify that this grammar accepts • aabb aaaabbbb • and rejects • aab aaaabbbbb A a B A b

Exercise 4: Beyond Regular Grammars • Extra Credit Homework Question (5pts) • write a similar grammar for the non-regular language • wwR • where w  {a,b}+, i.e. any non-empty sequence of a’s and b’s, and • wR is w in reverse order • Examples: • aabbaa w = aab wR = baa • aaaa w = aa wR = aa • *aaaaa • *abab

Homework Summary • 14 pts on offer • Exercise 1 (4pts) • Exercise 2 (4pts) • Exercise 3 (6pts) • Extra Credit • Exercise 4 (5pts)

LING 388: Language and Computers