CSC 333 T/F Questions
A Turing Machine can never write over an input symbol on the tape with a blank.
FALSE
A Turing Machine starts with its input already on its tape, and it will eventually halt, at which point it either accepts or rejects.
FALSE
B = {0^n 1^n | n > 0} is a regular language
FALSE
Every Context-Free Language is also Regular Language.
FALSE
For any Context-Free Language, there exists some DPDA (Deterministic PDA) that accepts the strings in that language, and no other strings.
FALSE
It is possible for an NFA or PDA to go into an infinite loop (possibly using epsilon transitions), meaning that it could neither accept or reject its input.
FALSE
Some non-deterministic TMs cannot be converted into a deterministic TM that recognizes the same language.
FALSE
The Halting Problem asks whether a TM can simulate another TM running on a given input. If this is possible, then the Halting Problem is decidable.
FALSE
The blank tape symbol of a Turing Machine is an element of the input alphabet, Σ.
FALSE
The class of problems called NP contains the class P but does not contain the class NP-Complete.
FALSE
The language { 〈k〉 | the Collatz sequence starting with k reaches 1 } is Turing decidable. Assume that n is given on the tape in binary notation. Note that it is unproven whether all Collatz sequences eventually reach 1.
FALSE
The tape of a Turing Machine is finite, so a TM can run out of tape.
FALSE
There are other models of computation in addition to Turing Machines, such as the Lambda Calculus and the Recursive Functions, but Turing Machines have proven to be more powerful than the other models.
FALSE
When a "Universal Turing Machine" (UTM) simulates another TM running on a given input, the UTM will always halt after a finite number of steps.
FALSE
{1^n 2^n 3^n | n > 0} is a context-free language over the alphabet Σ = {1, 2, 3}.
FALSE
A Turing Machine has a "tape alphabet" containing symbols (that it can read or write on the tape) which are not in the input alphabet Σ; additionally, the tape alphabet is denoted by Γ (Gamma), just like the "stack alphabet" of a PDA.
TRUE
A language like {a^n b^2n | n > 0}is Turing recognizable because there exists a TM that will do the following: (1) halt in an accept state if its input consists of some number of 'a' symbols, followed by the twice that number of 'b' symbols; and (2) halt in a reject state if the input is anything else.
TRUE
A multi-tape TM is no more powerful than a single tape TM, i.e. it can recognize the same set of languages.
TRUE
An NFA always halts, and when it does, it either accepts or rejects its input string.
TRUE
B = {0^n 1^m | n > 0, m > 0} is a regular language
TRUE
Currently, there are problems in the class NP for which there are no known polynomial-time solutions, so it appears that P ≠ NP.
TRUE
Define the description of a Turing machine to be (Q, Σ, Γ, b, δ, qH, F): this is a tuple of 7 items, where b is the blank symbol. Answer whether the description of a Turing Machine is finite.
TRUE
Every DPDA is also a PDA. (In other words, every DPDA meets all the criteria for being a PDA.)
TRUE
Every NFA has an equivalent DFA, i.e. there exists a DFA that accepts the same language.
TRUE
Every language recognized by a DPDA is a Context-Free Language.
TRUE
For any Regular Language, there exists a Turing Machine which will accept that language (rejecting strings not in the language), and which will always halt.
TRUE
For every problem X in the class NP, there exists a non-deterministic TM that decides X in a number of steps that is a polynomial in the size of the input.
TRUE
If a problem has an algorithm (i.e. a TM) that can produce a solution in a polynomial number of steps, then the problem is in the class P.
TRUE
If it turns out that P = NP, then the world will change in many ways, e.g. most cryptographic security will be breakable in polynomial time.
TRUE
The Halting Problem states that whether a given TM will halt on a given input is undecidable, meaning there cannot exist a TM that can simulate another TM and also always halt.
TRUE
The definition of a Context-Free Language is that there exists some PDA that accepts the strings in that language, and no other strings.
TRUE
The language { 〈k〉 | the Collatz sequence starting with k reaches 1 } is Turing recognizable. Note that〈n〉means an encoding of the number n, such as a binary encoding using 0s and 1s. Note that it is unproven whether all Collatz† sequences eventually reach 1.
TRUE
The set of strings generated by a CFG is a Context-Free Language.
TRUE
The stack of a PDA is unbounded; that is, it can grow arbitrarily large.
TRUE
We are using (in this class) a Turing Machine definition that says that a TM halts whenever it is in a state where it cannot make a transition (i.e. there is no applicable arrow, or maybe no arrow at all).
TRUE
We sometimes say computable as a synonym for decidable.
TRUE
When a Turing Machine starts, its input is already on the tape.
TRUE
While Sipser's definition allows only moving Right or Left, other definitions of Turing Machines allow an arrow to specify that the "tape head" does not move, such as the Turing Machine Simulator we are using in class.
TRUE
