10.5 Equivalence of Models
Detailed equivalence proofs between Turing machines, recursive functions, and lambda calculus, with explicit constructions and simulations.
8 notes
Detailed equivalence proofs between Turing machines, recursive functions, and lambda calculus, with explicit constructions and simulations.
Formal methods for comparing decision problems using many-one and Turing reducibility.
Machines that simulate any other Turing machine, establishing the concept of programmable computation.
Step-by-step evolution of Turing machine configurations and how computations are represented as traces.
Formal definition of Turing machines, including states, tape, alphabets, and transition functions.
Turing machine definitions, computation traces, universal machines, the halting problem, and undecidability results.
Turing machines, register machines, lambda calculus, recursive functions, and the precise mathematical models used to define computation.
The Church Turing thesis, formal models of computation, equivalence of models, and the distinction between mathematical theorem and foundational principle.