Order the class of languages in increasing order of power (Number them 1-4) • Context Free...
Order the class of languages in increasing order of power (Number them 1-4)
• Context Free
• Regular
• Turing Recongnizable
• Turing Decidable
Homework Answers
Order of the class of languages in increasing order of power (Number them 1-4)
1. Regular
2. Context Free
3. Turing decidable
4. Turing recognizable
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Order the class of languages in increasing order of power
(Number them 1-4)
• Context Free...
determine if the language is regular, context-free, Turing-decidable, or undecidable. For languages that are regular, give...
determine if the language is regular, context-free, Turing-decidable, or undecidable. For languages that are regular, give a DFA that accepts the language, a regular expression that generates the language, and a maximal list of strings that arc pairwise distinguishable with respect to the language. For languages that are context-free but not regular, prove that the language is not regular and either give a context- free grammar that generates the language or a pushdown automaton that accepts the language. You need...
determine if the language is regular, context-free, Turing-decidable, or undecidable. For languages that are regular, give...
determine if the language is regular, context-free, Turing-decidable, or undecidable. For languages that are regular, give a DFA that accepts the language, a regular expression that generates the language, and a maximal list of strings that are pairwise distinguishable with respect to the language. For languages that are context-free but not regular, prove that the language is not regular and either give a context- free grammar that generates the language or a pushdown automaton that accepts the language. You need...
2. Properties of the following: (a) Regular languages (b) Context-free languages (c) Regular expressions (d) Non-deterministic...
2. Properties of the following: (a) Regular languages (b) Context-free languages (c) Regular expressions (d) Non-deterministic finite automaton (e) Turing-recognizable and Turing-decidable languages (f) A <m B and what we can then determine (g) A <p B and what we can then determine (h) NP-hard and NP-complete.
Give examples of the following sets (languages): a. A set (language) that is Turing-recognizable but not...
Give examples of the following sets (languages): a. A set (language) that is Turing-recognizable but not decidable b. A set (language) that is decidable but not context-free c. A set (language) that is context-free but not regular
Determining whether languages are finite, regular, context free, or recursive 1. (Each part is worth 2 points) Fill in the blanks with one of the following (some choices might not be used): a) finit...
Determining whether languages are finite, regular, context free,
or recursive
1. (Each part is worth 2 points) Fill in the blanks with one of the following (some choices might not be used): a) finite b) regular but not finite d) context-free but not deterministic context-free e) recursive (that is, decidable) but not context-free f) recursively enumerable (that is, partially decidable) but not recursive g) not recursively enumerable Recall that if M is a Turing machine then "M" (also written as...
4. (Closure) Show that the class of context-free languages is closed under the star operation.
4. (Closure) Show that the class of context-free languages is closed under the star operation.
Show that the class of context-free languages is not closed under difference. Use either of the...
Show that the class of context-free languages is not closed under difference. Use either of the following facts: a. The class of context-free languages is not closed under intersection. b. The language {ww | w ∈ {a,b}*} is not a CFL.
Show that the class of context-free languages is closed under the regular operation union. For simplicity,...
Show that the class of context-free languages is closed under the regular operation union. For simplicity, you may assume that the alphabets of G1 and G2 are the same. [Hint: Use a constructive proof. Start with the formal definitions, G1 = (V1 ,∑, R1,S1) and G2 = (V2, ∑, R2, S2) and derive the formal definition of G∪.]
1. Show that the following languages are context-free. You can do this by writing a context...
1. Show that the following languages are context-free. You can do this by writing a context free grammar or a PDA, or you can use the closure theorems for context-free languages. For example, you could show that L is the union of two simpler context-free languages. (b) L {0, 1}* - {0"1" :n z 0}
determine if the language is regular, context-free, Turing-decidable, or undecidable. For languages that are regular, give a DFA that accepts the language, a regular expression that generates the language, and a maximal list of strings that arc pairwise distinguishable with respect to the language. For languages that are context-free but not regular, prove that the language is not regular and either give a context- free grammar that generates the language or a pushdown automaton that accepts the language. You need...
determine if the language is regular, context-free, Turing-decidable, or undecidable. For languages that are regular, give a DFA that accepts the language, a regular expression that generates the language, and a maximal list of strings that are pairwise distinguishable with respect to the language. For languages that are context-free but not regular, prove that the language is not regular and either give a context- free grammar that generates the language or a pushdown automaton that accepts the language. You need...
2. Properties of the following: (a) Regular languages (b) Context-free languages (c) Regular expressions (d) Non-deterministic finite automaton (e) Turing-recognizable and Turing-decidable languages (f) A <m B and what we can then determine (g) A <p B and what we can then determine (h) NP-hard and NP-complete.
Determining whether languages are finite, regular, context free,
or recursive
1. (Each part is worth 2 points) Fill in the blanks with one of the following (some choices might not be used): a) finite b) regular but not finite d) context-free but not deterministic context-free e) recursive (that is, decidable) but not context-free f) recursively enumerable (that is, partially decidable) but not recursive g) not recursively enumerable Recall that if M is a Turing machine then "M" (also written as...
1. Show that the following languages are context-free. You can do this by writing a context free grammar or a PDA, or you can use the closure theorems for context-free languages. For example, you could show that L is the union of two simpler context-free languages. (b) L {0, 1}* - {0"1" :n z 0}
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