22c:196:002 Logic in Computer Science
Spring 2007
Homework 4
Due: Fri, Mar 9, at 7pm
1 LTL Syntax
Do Problem 1 of Exercise 3.2 in Section 3.8 of the textbook.
2 LTL Syntax
For each of the statements below write an LTL formulas that best expresses the statement.
1. There is a state where both pand qhold.
2. It is always the case that if pholds in a state, then it holds in all the following states.
3. Either pnever holds or it holds infinitely often.
4. It is always the case that if pholds in a state then qholds in the following one.
5. It is always the case that if pholds in a state then qholds in the previous one.
6. It is always the case that if pholds in a state, then it holds in all the following states.
7. If pholds in the initial state then qnever holds.
3 LTL Semantics
Consider the model Min figure 3.39 on page 246 of the texbook, where the variables aand bare
written with an overbar in a state iff they are false in that state.
For each formula ϕbelow,
(i) describe a path form the initial state q3that satisfies ϕ, if any;
(ii) describe a path form the initial state q3that falsifies ϕ, if any.
If a requested satisfying or falsifying path does not exists, write “None”.
1. G a
2. a U b
3. X¬b∧G(¬a∨ ¬b)
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