Useful Links
Mathematics
Mathematical Logic
Computability Theory
Recursive Functions
Primitive Recursive Functions
Definition and Properties
Closure Properties
Base Functions
Zero Function
Successor Function
Projection Functions
Constructing New Functions
Composition
Primitive Recursion Schema
Examples
Addition
Multiplication
Factorial Function
Limitations
Non-expressibility of Certain Functions
Comparison with General Recursive Functions
μ-Recursive Functions
Definition and Characteristics
Inclusion of Minimization
μ-Operator and its Role
Comparison with Primitive Recursive Functions
Extension by Minimization
Expressiveness and Power
Examples
Computable Functions beyond Primitive
Solving Equations through Search
Equivalence to Turing Computability
Church-Turing Thesis
Constructive Proofs
Turing Machines
Definition and Components
Infinite Tape Concept
State Machine Model
Alphabet and Symbols
Transition Functions
Types of Turing Machines
Deterministic Turing Machines
Non-deterministic Turing Machines
Equivalence in Power to Deterministic
Universal Turing Machines
Concept of Universality
Simulation of Other Turing Machines
Decidability
Definition of Decidable Problems
Decision Problem Examples
Halting Problem
Membership Problem
Methods for Proving Decidability
Reductions
Recursive Algorithms
Undecidability
Definition and Recognition of Problems
Non-computable Functions
Rice's Theorem
Post Correspondence Problem
Implications of Undecidability
Limits of Algorithmic Solutions
Impact on Formal Systems
Complexity Theory
Theoretical Foundations
Definition of Complexity Classes
Measuring Computational Complexity
Time Complexity
Space Complexity
P vs NP Problem
P Class
Polynomial-Time Solvable Problems
Examples and Relevance
NP Class
Non-deterministic Polynomial-Time
Definition by Verification
NP-Complete Problems
Cook-Levin Theorem
Common Problems in NP-Complete
Implications and Significance
Computational Intractability
Open Questions in the Field
Complexity Class Hierarchies
P, NP, and co-NP
Polynomial Hierarchy
Exploration of PSPACE and EXPTIME
Reduction Techniques
Polynomial-time Reductions
Use in Proving Complexity Class Membership
Concepts of Completeness and Hardness
4. Set Theory
First Page
6. Applications