  Homework 6 (June 20) Material covered: Slides

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  Homework 6 (June 20) Material covered: Slides 10.4-12.9 1. Show that the following game is not static (by showing that it violates Definition 10.5.a): 2. Every elementary game is static. Explain why. 3. Consider the HPM of Slide 11.2. Assume the environment makes the move “0” at step #10 (ten), move “1” at step #10000 (ten thousand), and makes no other moves. What moves does the HPM make and at (at the beginning of) which steps? The count of steps starts from 0. Namely, step #0 is the time interval before the machine makes its first transition; step #1 is the time interval between the first and the second transitions; step # 2 is the time interval between the second and the third transitions; etc. 4. When do we say that a given HPM H computes (solves, wins) a given constant game G ? [Slide 11.3] 5. What is an algorithmic solution, or an algorithmic winning strategy, for a constant static game G? [Slide 11.6] 6. When do we say that a given constant static game (computational problem) is computable ? [Slide 11.6] 7. What is a logical (or uniform) solution of a given sentence F ? [Slide 12.4] 8. When do we say that a given sentence F is logically (or uniformly) valid ? [Slide 12.4] 9. When do we say that a given sentence F is nonlogically (or multiformly) valid ? [Slide 12.4] 10. Which of the following two statements is true of all sentences F and why ? (i) If F is logically valid, then it is also nonlogically valid. (ii) If F is nonlogically valid, then it is also logically valid. 11. One of the statements of the above Question 10 is false for some sentences. Write three such sentences.