### NP is the class of languages that have polynomial time verifiers

The class NP, which stands for "nondeterministic polynomial time," is a fundamental concept in computational complexity theory, a subfield of theoretical computer science. To understand NP, one must first grasp the notion of decision problems, which are questions with a yes-or-no answer. A language in this context refers to a set of strings over some

- Published in Cybersecurity, EITC/IS/CCTF Computational Complexity Theory Fundamentals, Complexity, Definition of NP and polynomial verifiability

### Is there a contradiction between the definition of NP as a class of decision problems with polynomial-time verifiers and the fact that problems in the class P also have polynomial-time verifiers?

The class NP, standing for Non-deterministic Polynomial time, is central to computational complexity theory and encompasses decision problems that have polynomial-time verifiers. A decision problem is one that requires a yes-or-no answer, and a verifier in this context is an algorithm that checks the correctness of a given solution. It’s crucial to distinguish between solving

### Is verifier for class P polynomial?

A verifier for class P is polynomial. In the field of computational complexity theory, the concept of polynomial verifiability plays a crucial role in understanding the complexity of computational problems. To answer the question at hand, it is important to first define the classes P and NP. The class P, also known as "polynomial time,"

- Published in Cybersecurity, EITC/IS/CCTF Computational Complexity Theory Fundamentals, Complexity, Definition of NP and polynomial verifiability

### Can a Nondeterministic Finite Automaton (NFA) be used to represent the state transitions and actions in a firewall configuration?

In the context of firewall configuration, a Nondeterministic Finite Automaton (NFA) can be used to represent the state transitions and actions involved. However, it is important to note that NFAs are not typically used in firewall configurations, but rather in the theoretical analysis of computational complexity and formal language theory. An NFA is a mathematical

- Published in Cybersecurity, EITC/IS/CCTF Computational Complexity Theory Fundamentals, Finite State Machines, Introduction to Nondeterministic Finite State Machines

### Is using three tapes in a multitape TN equivalent to single tape time t2(square) or t3(cube)? In other words is the time complexity directly related to number of tapes?

Using three tapes in a multitape Turing machine (MTM) does not necessarily result in an equivalent time complexity of t2(square) or t3(cube). The time complexity of a computational model is determined by the number of steps required to solve a problem, and it is not directly related to the number of tapes used in the

### If the value in the fixed point definition is the lim of the repeated application of the function can we call it still a fixed point? In the example shown if instead of 4->4 we have 4->3.9, 3.9->3.99, 3.99->3.999, … is 4 still the fixed point?

The concept of a fixed point in the context of computational complexity theory and recursion is an important one. In order to answer your question, let us first define what a fixed point is. In mathematics, a fixed point of a function is a point that is unchanged by the function. In other words, if

- Published in Cybersecurity, EITC/IS/CCTF Computational Complexity Theory Fundamentals, Recursion, The Fixed Point Theorem

### How big is the stack of a PDA and what defines its size and depth?

The size of the stack in a Pushdown Automaton (PDA) is an important aspect that determines the computational power and capabilities of the automaton. The stack is a fundamental component of a PDA, allowing it to store and retrieve information during its computation. Let us explore the concept of the stack in a PDA, discuss

- Published in Cybersecurity, EITC/IS/CCTF Computational Complexity Theory Fundamentals, Pushdown Automata, PDAs: Pushdown Automata

### Are there current methods for recognizing Type-0? Do we expect quantum computers to make it feasible?

Type-0 languages, also known as recursively enumerable languages, are the most general class of languages in the Chomsky hierarchy. These languages are recognized by Turing machines that can accept or reject any input string. In other words, a language is Type-0 if there exists a Turing machine that halts and accepts any string in the

### Why LR(k) and LL(k) are not equivalent?

LR(k) and LL(k) are two different parsing algorithms used in the field of computational complexity theory to analyze and process context-free grammars. While both algorithms are designed to handle the same type of grammars, they differ in their approach and capabilities, leading to their non-equivalence. The LR(k) parsing algorithm is a bottom-up approach, meaning it

### Is there a class of problems which can be described by deterministic TM with a limitation of only scanning tape in right direction and never going back (left)?

Deterministic Turing Machines (DTMs) are computational models that can be used to solve various problems. The behavior of a DTM is determined by a set of states, a tape alphabet, a transition function, and initial and final states. In the field of computational complexity theory, the time complexity of a problem is often analyzed in