Suppose we augment the definition of Turing machines so that in addition toqacceptandqreject, a TM also has a halting stateqerror, which represents a runtime error.Say that a TM is buggy iff there exists an input that causes itto enterqerror. Prove thathMi:Mis buggyis undecidable. (This is not just an academic exercise. By the ChurchTuring thesis, this means its impossible to write a programthat can take the source code ofanother program and determine whether it could possibly have a runtime error.

3. [20 points] Suppose we augment the definition of Turing machines so that in addition to Qaccept and qreject, a TM also has a halting state gerror, which represents a runtime error Say that a TM is "buggy" iff there exists an input that causes it to enter qerror. Prove that M) : M is buggy} is undecidable. (This is not just an academic exercise. By the Church- Turing thesis, this means it's impossible to write a program that can take the source code of 03 another program and determine whether it could possibly have a runtime error.) 3. [20 points] Suppose we augment the definition of Turing machines so that in addition to Qaccept and qreject, a TM also has a halting state gerror, which represents a runtime error Say that a TM is "buggy" iff there exists an input that causes it to enter qerror. Prove that M) : M is buggy} is undecidable. (This is not just an academic exercise. By the Church- Turing thesis, this means it's impossible to write a program that can take the source code of 03 another program and determine whether it could possibly have a runtime error.)