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 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
Can a turing machine move the head over the tape by more than one cell at each step of their operation
A Turing machine, as originally conceived by Alan Turing in 1936, operates on a tape divided into discrete cells, each capable of holding a symbol from a finite alphabet. The machine has a head that can read and write symbols on the tape and move left or right one cell at a time. This fundamental
- Published in Cybersecurity, EITC/IS/CCTF Computational Complexity Theory Fundamentals, Turing Machines, Turing Machines as Problem Solvers
Are Turing machines and lambda calculus equivalent in computational power?
The question of whether Turing machines and lambda calculus are equivalent in computational power is a fundamental one in theoretical computer science. Both formalisms are central to the study of computation and have been extensively analyzed for their capabilities and limitations. The equivalence of these two models of computation is a cornerstone of our understanding
- Published in Cybersecurity, EITC/IS/CCTF Computational Complexity Theory Fundamentals, Turing Machines, Definition of TMs and Related Language Classes
What is the concept of decidability in the context of computational complexity theory?
Decidability, in the context of computational complexity theory, refers to the ability to determine whether a given problem can be solved by an algorithm. It is a fundamental concept that plays a important role in understanding the limits of computation and the classification of problems based on their computational complexity. In computational complexity theory, problems
What is the Church-Turing thesis and how does it relate to algorithms and Turing machines?
The Church-Turing thesis is a fundamental concept in the field of computational complexity theory, specifically in relation to algorithms and Turing machines. It is named after Alonzo Church and Alan Turing, who independently formulated the thesis in the 1930s. The Church-Turing thesis states that any function that can be effectively computed by an algorithm can
What is the Church-Turing Thesis and how does it define computability?
The Church-Turing Thesis is a fundamental concept in the field of computational complexity theory, which plays a important role in understanding the limits of computability. It is named after the mathematician Alonzo Church and the logician and computer scientist Alan Turing, who independently formulated similar ideas in the 1930s. At its core, the Church-Turing Thesis