How can I show that a language is Turing-recognizable and decidable? I was wondering how I can show that the language $\{a^n b^n c^n \mid n \geq 0 \}$ is Turing-recognizable. Also, if it is Turing-decidable?
A language is Turing decidable if you can write a C program (replace C with your favorite programming language) that outputs YES if the input belongs to the language and outputs NO otherwise. It is Turing recognizable if in the latter case the C program simply never halts.