Decidability

Theorem:

A (DFA)  is a decidable language (accept)

Theorem:

       A (NFA) is a decidable language (accept)

Theorem:

       E (DFA) is a decidable language (empty)

Theorem:

       EQ (DFA) is a decidable language (equal)

Theorem:

       A (CFG) is a decidable language (accept)

Theorem:

       E (CFG) is a decidable language (empty)

 

Theorem:

       A (TM) is an undecidable language (accept)

       The diagonalization method

R is uncountable

 

Some language is not Turing recognizable

       The set of all Turing machines is countable

       The set of all languages is uncountable.

 

Theorem:

       A language is decidable if and only if it is both Turing-recognizable and co-Turing recognizable

       A(TM)    is not Turing recognizable.