Chapter 1: Computability
-recursive functions are computable - program construction
- loop until
- might never terminate
- increment
- loop until
- program construction
- all computable functions are
-recursive - belief
- encoding URM programs to natural numbers
- prime factorisation
- encoding URM states (same sequence encoding)
- semi-decidable sets
- Recursively Enumerable Language
- Semi-decidable Predicate
- finite sets are semi-decidable (big switch statement)
Chapter 2: Propositional Logic
- Propositional Logic
- Set of all propositional well-formed formulas is decidable
- “Belegung” → variable assignment
- “Wahrheitsfunktion” → Interpretation
- Differentiation: language symbol
and Boolean function - Für jede Belegung
gibt es genau eine Wahrheitsfunktion , wobei , d.h., .