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Revision CSE2303 Formal Methods I Lecture 24

Overview What you DON’T need to know for the exam. What you DO need to know for the exam. Exam Technique.

What you DON’T need to know C flex/lex bison/yacc sicstus/prolog How to build a UTM. How to convert WFF into clauses.

Exam Questions Will be like the tutorial sheet questions. You need to be able to do ALL the questions on ALL the tutorial sheets. Solutions to these questions are available on the web via:

What you need to know

Regular Languages Regular Expressions –How to define a language using a regular expression. –Determine whether a string can be defined by a regular expression. –Properties of Regular Languages, e.g. the complement of a regular language is a regular language. Finite Automata –Know how they work. –Construct a finite automata which accepts a language. –How to construct a finite automata for the complement of a language.

Regular Language (cont.) Nondeterministic Finite Automata –Know how they work. –Construct NFA-  which accepts a language defined by a regular expression. –Convert a NFA-  into a finite automata. Generalised Transition Graph –Know how they work. –Convert into a regular expression. Moore & Mealy machines –Know how they work. –Find equations for a sequential circuit corresponding to a Mealy machine. Pumping Lemma –What is an application of the Pumping Lemma

Problem Construct a finite automata which accepts the languages defined by the regular expression (a + b)(aa + ab)*

Context-free Languages Context Free Grammar –How to show a CFG is ambiguous. –Find a parse tree for a word generated by a CFG. –Find rightmost and leftmost derivations of a word generated by a CFG. –Know examples of CFLs. –How to write a regular grammar for a regular language. Pushdown Automata –How to trace the execution of a word through a PDA. Pumping Lemma –What is an application of the Pumping Lemma.

Problem Construct a regular grammar which accepts the languages defined by the regular expression (a + b)(aa + ab)*

Problem For the following CFG S  E E  T + E | T - E | T T  F*T | F/T | F F  integer | (E) find the parse tree for the expression 2-3*4/7

Recursive-Enumerable Turing Machines –Build a Turing Machine which accepts a language. Recursive-Enumerable & Recursive –Definition and Examples. Computable Functions –Definition and examples. –Build a Turing machine which computes a function.

Problem Build a Turing Machine that accepts the language {a n b 2n }.

Logic Propositional Logic –Express arguments in propositional logic. –Determine whether an argument is valid. –Find CNF and clausal form of formulae. –Be able to do resolution. Predicate Logic –Express statements in predicate logic. –Be able to do resolution.

Problem For the following formula ((p  q)  (q  p))  r Find the CNF.

Problem Convert the following statements into first order logic, using the constants mary and peter, the function rightFoot, and the predicate kicked. 1. The Peter’s right foot kicked Mary’s right foot. 2. No one kicked Peter.

Problem Using resolution show that the following set of clauses are unsatisfiable. Clearly indicate at each step which clauses you are resolving and what unifications you are making. {{p(X)}, {q(Y, a), ¬p(a)}, {¬q(a,a)}}

Exam Technique DON’T PANIC Use the reading time. Look for the easy marks, and do those questions first. Don’t spend too much time on any question.