### Can every arbitrary problem be expressed as a language?

In the domain of computational complexity theory, the concept of expressing problems as languages is fundamental. To address this question we need to consider theoretical underpinnings of computation and formal languages. A "language" in computational complexity theory is a set of strings over a finite alphabet. It is a formal construct that can be recognized

- Published in Cybersecurity, EITC/IS/CCTF Computational Complexity Theory Fundamentals, Introduction, Theoretical introduction

### Is P complexity class a subset of PSPACE class?

In the field of computational complexity theory, the relationship between the complexity classes P and PSPACE is a fundamental topic of study. To address the query regarding whether the P complexity class is a subset of the PSPACE class or if both classes are the same, it is essential to delve into the definitions and

### Does every multi-tape Turing machine has an equivalent single-tape Turing machine?

The question of whether every multi-tape Turing machine has an equivalent single-tape Turing machine is important one in the field of computational complexity theory and the theory of computation. The answer is affirmative: every multi-tape Turing machine can indeed be simulated by a single-tape Turing machine. This equivalence is crucial for understanding the computational power

- Published in Cybersecurity, EITC/IS/CCTF Computational Complexity Theory Fundamentals, Turing Machines, Multitape Turing Machines

### What are the outputs of predicates?

First-order predicate logic, also known as first-order logic (FOL), is a formal system used in mathematics, philosophy, linguistics, and computer science. It extends propositional logic by incorporating quantifiers and predicates, which allows for a more expressive language capable of representing a wider array of statements about the world. This logical system is foundational in various

### Are lambda calculus and turing machines computable models that answers the question on what does computable mean?

Lambda calculus and Turing machines are indeed foundational models in theoretical computer science that address the fundamental question of what it means for a function or a problem to be computable. Both models were developed independently in the 1930s—lambda calculus by Alonzo Church and Turing machines by Alan Turing—and they have since been shown to

- Published in Cybersecurity, EITC/IS/CCTF Computational Complexity Theory Fundamentals, Turing Machines, The Church-Turing Thesis

### Can we can prove that Np and P class are thesame by finding an efficient polynomial solution for any NP complete problem on a deterministic TM

The question of whether the classes P and NP are equivalent is one of the most significant and long-standing open problems in the field of computational complexity theory. To address this question, it is essential to understand the definitions and properties of these classes, as well as the implications of finding an efficient polynomial-time solution

- Published in Cybersecurity, EITC/IS/CCTF Computational Complexity Theory Fundamentals, Complexity, Time complexity classes P and NP

### Can there exist a turing machine that would be unchanged by the transformation?

To address the question of whether there can exist a Turing machine that would remain unchanged by a transformation, it is essential to delve into the fundamentals of Turing machines, their theoretical underpinnings, and the nature of transformations within the context of computational theory. ### Turing Machines: An Overview A Turing machine, as conceptualized by

### Are the set of all languages uncountable infinite?

The question "Are the set of all languages uncountable infinite?" touches upon the foundational aspects of theoretical computer science and computational complexity theory. To address this question comprehensively, it is essential to delve into the concepts of countability, languages, and sets, as well as the implications these have in the realm of computational theory. In

### What is rules of inference of deduction?

In the domain of logic, particularly within the realms of computational complexity theory and cybersecurity, the concept of rules of inference holds paramount importance. Rules of inference, also known as inference rules, are fundamental principles that dictate the valid transitions from premises to conclusions within a formal system. These rules are the backbone of deductive

### Can a turing machine decide and recognise a language and also compute a function?

A Turing machine (TM) is a theoretical computational model that plays a central role in the theory of computation and forms the foundation for understanding the limits of what can be computed. Named after the British mathematician and logician Alan Turing, the Turing machine is an abstract device that manipulates symbols on a strip of

- Published in Cybersecurity, EITC/IS/CCTF Computational Complexity Theory Fundamentals, Turing Machines, Definition of TMs and Related Language Classes