Theory of Computation: Question Set – 28
What is the difference between the P, NP, and NP-complete complexity classes?
The P complexity class consists of problems that can be solved in polynomial time by a deterministic Turing machine. The NP complexity class consists of problems that can be solved in polynomial time by a non-deterministic Turing machine, or verified in polynomial time by a deterministic Turing machine. The NP-complete complexity class consists of the hardest problems in NP, which are also believed to be the hardest problems in all of NP.
What is the difference between an oracle machine and a standard Turing machine?
An oracle machine is a theoretical model of a Turing machine that has access to an oracle, which is a black box that can solve a certain problem in constant time. This allows the machine to solve certain problems much more quickly than a standard Turing machine, which can only solve problems by performing individual steps.
What is the difference between a reduction and a complete problem?
A reduction is a technique used in the theory of computation to show that one problem can be transformed into another problem in a certain way. A complete problem is a problem that is as hard as the hardest problems in a certain complexity class, in the sense that any problem in the class can be reduced to it in polynomial time.
What is the difference between the halting problem and Rice’s theorem?
The halting problem is the problem of determining whether a program will halt or run forever on a given input. Rice’s theorem states that any non-trivial property of the behavior of a program is undecidable, which means that there is no algorithmic solution to many important problems in program analysis and verification.
What is the difference between a one-way function and a trapdoor function?
A one-way function is a function that is easy to compute in one direction but hard to invert in the other direction, without knowledge of a secret key. A trapdoor function is a one-way function that also has a secret trapdoor that allows it to be easily inverted by someone who has the key.
What is the difference between a cryptographic hash function and a symmetric-key encryption algorithm?
A cryptographic hash function is a one-way function that maps an input of arbitrary size to a fixed-size
What is the difference between a Turing machine and a finite automaton?
A Turing machine is a theoretical model of a computer that can read and write to an infinite tape, while a finite automaton is a theoretical model of a computer that has a fixed number of states and transitions based on input. Turing machines are more powerful than finite automata, as they can simulate any algorithm that can be executed by a computer.
What is the Church-Turing thesis?
The Church-Turing thesis is a hypothesis that states that any algorithmic problem that can be solved by a computer can be solved by a Turing machine. This hypothesis has not been formally proven, but is widely accepted as true by computer scientists.