20 Theory of Computation Interview Questions and Answers

Theory of Computation is the study of the limits of computational power and efficiency. It is a branch of mathematics that is relevant to the field of computer science. Many employers will ask questions about your understanding of theory of computation during a job interview, in order to gauge your theoretical knowledge and problem-solving abilities. In this article, we review some common questions you may encounter during your interview.

Theory of Computation Interview Questions and Answers

Here are 20 commonly asked Theory of Computation interview questions and answers to prepare you for your interview:

1. What is theory of computation?

Theory of computation is the study of the limitations of algorithms and computational models. It is also known as the theory of automata or the theory of formal languages.

2. Can you explain what a Turing Machine is?

A Turing Machine is a hypothetical machine that is able to simulate the behavior of any other machine. It is used as a model for understanding the limits of what computers can and cannot do.

3. What are the building blocks that make up a Turing Machine?

The building blocks of a Turing Machine are the states, the transition function, the input, and the output. The states are the different configurations that the machine can be in. The transition function is what determines how the machine moves from one state to another. The input is what is fed into the machine, and the output is what the machine produces.

4. How can you represent a Turing machine as a function?

A Turing machine can be represented as a function that takes in an input string and outputs a new string, or it can be represented as a function that takes in an input string and outputs a 1 or a 0 depending on whether or not the string is accepted by the machine.

5. Is it possible to convert a Turing machine into a mathematical function? If yes, then how?

Yes, it is possible to convert a Turing machine into a mathematical function. This can be done by mapping the Turing machine’s states and transitions to a function’s domain and codomain.

6. Can you explain what an NFA is and why they’re important?

NFA stands for “nondeterministic finite automaton.” They are important in the theory of computation because they provide a way to model systems with nondeterministic behavior. This means that they can be used to represent systems where there is more than one possible outcome for a given input.

7. Can you explain what a DFA is and why they’re important?

A DFA is a deterministic finite automaton, which is a machine that can be in one of a finite number of states and that can transition from one state to another in a deterministic way. DFAs are important because they can be used to model any system that can be in one of a finite number of states and that has a finite number of inputs.

8. What’s the difference between a DFA and an NFA? Which one do you think is better?

A DFA is a deterministic finite automaton, while an NFA is a nondeterministic finite automaton. A DFA is better in that it is more predictable and easier to understand, while an NFA is more powerful and can recognize more complex patterns.

9. Can you explain what regular expressions are? Why are they important in the context of automata and formal languages?

Regular expressions are a way of describing patterns in strings. They are important in the context of automata and formal languages because they can be used to describe the set of all strings that a particular automaton or formal language will accept.

10. What are some real-world applications for finite state machines?

Finite state machines can be used for a variety of tasks, including modeling computer hardware, designing computer programs, and creating efficient algorithms.

11. What does it mean if something is decidable or undecidable?

A decidable problem is one where it is possible to write an algorithm that will always produce the correct answer, while an undecidable problem is one where it is not possible to write such an algorithm. For example, the problem of whether or not a given program will eventually halt is undecidable, because there is no way to know for sure whether or not a program will halt without actually running it.

12. What is the significance of the halting problem?

The halting problem is a problem in computer science that is used to show that certain problems are unsolvable. In particular, it is used to show that there is no algorithm that can take in a description of a program and an input and always correctly say whether or not the program will halt when run with that input. This is significant because it shows that there are some problems that computers will never be able to solve.

13. Can you give me some examples of problems that are not solvable by a turing machine?

Some examples of problems that are not solvable by a turing machine include the halting problem, the satisfiability problem, and the problem of finding the shortest path between two points.

14. Can you explain how to use a pushdown stack in a Turing machine?

A pushdown stack is a data structure that allows for the storage of data in a last-in, first-out (LIFO) manner. This means that the most recently added data will be the first data to be removed. In a Turing machine, a pushdown stack can be used to store the machine’s current state, as well as any data that the machine needs to remember.

15. What do you know about linear bounded automata?

Linear bounded automata are a type of automaton that runs on a tape, which is divided into sections called cells. The automaton can only move forwards or backwards along the tape, and can only read or write to the cell it is currently on. The automaton is said to be “bounded” because there is a limit to how far it can move in either direction.

16. Can you explain how to create a deterministic pushdown automaton?

A deterministic pushdown automaton (DPDA) is a type of pushdown automaton that can be used to process deterministic context-free languages. In order to create a DPDA, you need to first specify a finite set of states, a finite set of input symbols, a finite set of stack symbols, a transition function, a start state, and a final state. The transition function will take as input a state and an input symbol, and will output a new state and a symbol to be pushed onto the stack. The start state is the initial state of the automaton, and the final state is the state that the automaton will enter when it has successfully processed an input string.

17. What are some different types of computable functions?

There are many different types of computable functions, but some of the most common are the Turing machine, the Post machine, and the recursive function.

18. What are some limitations of finite state machines?

One of the main limitations of finite state machines is that they can only process regular languages. This means that they are not powerful enough to process certain types of languages, such as context-free languages. Additionally, finite state machines can only keep track of a limited amount of information, so they are not well-suited for tasks that require a lot of memory.

19. Can you give me some examples of problems that are not solvable by a finite state machine?

Some examples of problems that are not solvable by a finite state machine include the halting problem, the satisfiability problem, and the Post’s correspondence problem.

20. What is the computational class P?

P is the class of problems that can be solved by a deterministic Turing machine in polynomial time.