{
"translations": {
"en": {
"RL": {
"type": "select",
"description": "Regular Grammars are another way to define a regular language.",
"question":"What are Regular Languages?",
"answer": ["Languages accepted by DFAs", "Languages accepted by NFAs", "Languages represented by Regular Expressions"],
"choices": ["Languages accepted by DFAs", "Languages accepted by NFAs", "Languages represented by Regular Expressions", "Natural Languages"]
},
"RG": {
"type": "select",
"description": "A Regular Grammar is a special type of grammar.",
"question": "What is true about grammars?",
"answer": ["They are used to define languages", "Grammar $G$ can be defined as $G = (V, T, S, P)$"],
"choices": ["They are used to define languages", "They are used to accept Languages", "Grammar $G$ can be defined as $G = (V, T, S, P)$"],
"correctFeedback": ["Machines (like DFAs and NFAs) accept languages, while grammars define or describe them."]
},
"variable": {
"type": "select",
"description": "Suppose we have the grammar $G = (V, T, S, P)$",
"question": "What is $V$?",
"answer": ["Variables", "Non-Terminals"],
"choices": ["Variables", "Terminals", "Start Variable", "Production set", "Non-Terminals", "Replacement Rules"],
"incorrectFeedback": ["Did you pick everything that $V$ is?"]
},
"terminal": {
"type": "select",
"description": "Suppose we have the grammar $G = (V, T, S, P)$ where
$V =$ variables (or non-terminals) $= A, B, \\ldots Z$",
"question": "What is T?",
"answer": ["Terminals"],
"choices": ["Variables", "Terminals", "Start Variable", "Production set", "Non-Terminals", "Replacement Rules"],
"incorrectFeedback": ["Don't pick too many!"]
},
"production": {
"type": "select",
"description": "Suppose we have the grammar $G = (V, T, S, P)$ where
$V =$ variables (or non-terminals) $= A, B, \\ldots, Z$
$T =$ terminals $= a, b, \\ldots, z, 0, 1, \\ldots 9$",
"question": "What is P?",
"answer": ["Production set", "Replacement Rules"],
"choices": ["Variables", "Terminals", "Start Variable", "Production set", "Non-Terminals", "Replacement Rules"]
},
"start": {
"type": "select",
"description": "Suppose we have the grammar $G = (V, T, S, P)$ where
$V =$ variables (or non-terminals) $= A, B, \\ldots, Z$
$T =$ terminals $= a, b, \\ldots, z, 0, 1, \\ldots 9$
$P =$ productions (replacement rules)",
"question": "What is S?",
"answer": ["Start Variable"],
"choices": ["Variables", "Terminals", "Start Variable", "Production set", "Non-Terminals"]
},
"sets": {
"type": "select",
"description": "Suppose we have the grammar $G = (V, T, S, P)$ where
$V =$ variables (or non-terminals) $= A, B, \\ldots, Z$
$T =$ terminals $= a, b, \\ldots, z, 0, 1, \\ldots 9$
$P =$ productions (replacement rules)
$S =$ start symbol",
"question": "Select all the things in the definition that are sets.",
"answer": ["$V$", "$T$", "$P$"],
"choices": ["$V$", "$T$", "$S$", "$P$"]
},
"linear": {
"type": "select",
"description": "Definition: A grammar is linear if has a single variable in the RHS of every production rule (and consists of a single variable on the LHS of every production rule).
So, all productions are of one of these forms:
$A \\rightarrow xB$
$A \\rightarrow Cx$
$A \\rightarrow x$
where $A, B, C \\in V, x \\in \\ T^*$",
"question": "Why is the grammar shown to the left considered linear?",
"answer": ["Each production rule has at most one variable on the RHS", "Each production rule has a single variable on the LHS"],
"choices": ["Each production rule has at most one variable on the RHS", "Each production rule has a single variable on the LHS"],
"correctFeedback": ["This might seem odd that we are saying that the LHS must be a single variable. But some types of grammars are allowed to have more than one symbol (terminals or non-termals) on the left-hand side. Of course, these are not linear, or even regular."]
},
"right": {
"type": "select",
"description": "Definition: A Right-linear grammar is a special case of a linear grammar. A Right-linear grammar is linear, and if there is a variable on the LHS of a production, then it always occurs at the right end of the rule. For example, this grammar is right-linear:
$A \\rightarrow xB$
$A \\rightarrow xC$
$A \\rightarrow y$
where $A, B, C \\in V$ and $x, y \\in T^*$",
"question": "Why is the grammar shown on the left right linear?",
"answer": ["Any production rule with a variable on the RHS has that variable at the right end of the RHS","Each production rule has at most one variable on the LHS"],
"choices": ["Each production rule has at most one variable on the RHS",
"Each production rule has at most one variable on the LHS",
"Any production rule with a variable on the RHS has that variable at the right end of the RHS",
"Any production rule with a variable on the RHS has that variable at the left end of the RHS"]
},
"left": {
"type": "select",
"description": "A left-linear grammar is simmilar to a right-linear grammar. But in each production rule the occurance of any variable on the RHS, if there is one, is at the begining of the RHS. For example,
$A \\rightarrow Bx$
$A \\rightarrow Cy$
$A \\rightarrow x$
where $A, B, C \\in V, x, y \\in T^*$",
"question": "Why is the grammar shown on the left left linear?",
"answer": ["Any production rule with a variable on the RHS has that variable at the left end of the RHS","Each production rule has at most one variable on the LHS"],
"choices": ["Each production rule has at most one variable on the RHS",
"Each production rule has at most one variable on the LHS",
"Any production rule with a variable on the RHS has that variable at the right end of the RHS",
"Any production rule with a variable on the RHS has that variable at the left end of the RHS"]
},
"regular": {
"type": "select",
"description": "Definition: A regular grammar is right-linear OR left-linear.",
"question":"What is the type of the following grammar?
G = ($\\{S\\}, \\{a,b\\}$,S,P),
P =
$S \\ \\rightarrow abS$
$S \\ \\rightarrow \\ \\lambda$
$S \\ \\rightarrow Sab$",
"answer": ["Linear Grammar"],
"choices": ["Left-Linear Grammar", "Right-Linear Grammar", "Linear Grammar", "Regular Grammar", "Non-Linear Grammar"],
"correctFeedback": ["This grammar is linear, because every rule is of the right form. BUT, it is not regular. Because a regular grammar cannot mix right-linear and left-linear rules."]
},
"Ex2": {
"type": "select",
"description": "Definition: A regular grammar is right-linear OR left-linear.",
"question":"What is the type of the following grammar?
G = ($\\{S\\}, \\{a,b\\}$,S,P),
P =
$S \\ \\rightarrow abS$
$S \\ \\rightarrow \\ \\lambda$
$S \\ \\rightarrow aS$",
"answer": ["Right-Linear Grammar", "Regular Grammar", "Linear Grammar"],
"choices": ["Left-Linear Grammar", "Right-Linear Grammar", "Linear Grammar", "Regular Grammar", "Non-Linear Grammar"]
},
"Ex3": {
"type": "select",
"description": "Definition: A regular grammar is right-linear OR left-linear.",
"question":"What is the type of the following grammar?
G = ($\\{S\\}, \\{a,b\\}$,S,P),
P =
$S \\ \\rightarrow Sab$
$S \\ \\rightarrow \\ \\lambda$
$S \\ \\rightarrow Sa$",
"answer": ["Left-Linear Grammar", "Regular Grammar", "Linear Grammar"],
"choices": ["Left-Linear Grammar", "Right-Linear Grammar", "Linear Grammar", "Regular Grammar", "Non-Linear Grammar"]
},
"Ex4": {
"type": "select",
"description": "Definition: A regular grammar is right-linear OR left-linear.",
"question":"What is the type of the following grammar?
G = ($\\{S\\}, \\{a,b\\}$,S,P),
P = $S \\ \\rightarrow abS\\mid \\lambda \\mid aS$",
"answer": ["Right-Linear Grammar", "Regular Grammar", "Linear Grammar"],
"choices": ["Left-Linear Grammar", "Right-Linear Grammar", "Linear Grammar", "Regular Grammar", "Non-Linear Grammar"],
"correctFeedback": ["This is just a shorter way to write the three prodcution rules for $S$ on one line."]
}
}
}
}