L2 says m no. Their concatenation first matches no. So it can be decided by TM. L2 says any no. Their intersection says n no. So it can be decided by turing machine, hence recursive. For every non-deterministic TM, there exists an equivalent deterministic TM. Turing recognizable languages are closed under union and complementation.
Turing decidable languages are closed under intersection and complementation. Turing recognizable languages are closed under union and intersection. Skip to content. Change Language. Related Articles. Regular expression, languages, grammar and finite automata. Context free languages, grammar and push down automata.
Context Sensitive langauges. Turing machines. TOC Quizes. Table of Contents. Improve Article. Ask yourself what formal automaton can simulate generation of context sensitive language and what is used to generate recursive language.
Then just try to simulate one using the other. Once you look up the right automata in your textbook, you will sure be able to prove what you want. You dont have to assume this, refer to Peter Linz's book for proof. To recognize a recursive language you need a kind of automaton named Decider. It is exactly a Turing Machine tricked by a limited control flow, that is, to ensure it will always halt.
Concerning context-sensitive languages, they are indeed a proper subset of recursive ones. It's trivial giving that the minimal automaton to recognize a context-sensitive language, a Linear bounded automaton is strictly less powerful than a decider.
I guess that it would also be possible to demonstrate based on grammar restriction rules. According to Papadimitriou's book 3. So, yes, your assumption is correct. As per my references , I would also say that Context Sensitive Languages are a proper subset of a set of all Recursive Languages. You can find this proof in any Standard Textbook like. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Collectives on Stack Overflow.
Learn more. Recursive languages vs context-sensitive languages Ask Question. Asked 11 years, 7 months ago. Active 1 year, 11 months ago. Viewed 5k times. Improve this question. Martin Konecny Martin Konecny Add a comment. Active Oldest Votes.
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