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Homework Exercise 3

Due: by 2pm on Web 15 Oct
Worth: 1.5%

For each question, please write up detailed answers carefully: make sure that you use notation and terminology correctly, and that you explain and justify what you are doing. Marks will be deducted for incorrect or ambiguous use of notation and terminology, and for making incorrect, unjustified, ambiguous, or vague claims in your solutions.

1. Is the following language decidable, undecidable but recognizable, or unrecognizable? Prove your answer.

   BA_TM = { <M,w,t> : M is a TM that accepts input w within t steps of computation }

2. Is the following language decidable, undecidable but recognizable, or unrecognizable? Prove your answer.

   NL_TM = { <M,w> : M is a TM whose head never moves left during its computation on input w }