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0
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2answers
11 views

Relation between CLR Grammar and Ambiguity

I am studying CLR Parser and have a query about Grammar. If a Grammar can't be parsed using CLR(1) Parser ( i.e LR(1)) parser is it necessarily ambiguous? Is it possible that a grammar which is ...
0
votes
1answer
27 views

Help me find the ambiguity in this grammar

I've been sitting on this for 20+ minutes and can't seem to generate a string that is ambiguous. Can anyone help me? The grammar is: $$S \xrightarrow{} SS \mid T$$ $$T \xrightarrow{} aTb \mid ab $$ ...
2
votes
2answers
44 views

Context-free grammars and priority

This grammar is supposed to give priority to multiplication: E -> E + T | T. T -> T * F | F. F -> x. A derivation for "x + x * x" would be (unless I'm wrong): E => E + T => T + T => F + T => x + ...
0
votes
1answer
25 views

Is a grammar that accepts function declarations, function calls and expressions (at any order!) necessarily cyclic?

As the title suggests, assume a grammar which has to recognize function declarations, function calls, and expressions, at any order. Does that mean it has to be cyclic, and therefore ambiguous? I ...
0
votes
0answers
45 views

Can we say we reduced a rule if we reduced an equivalent set of smaller rules?

I have constructed an SLR(1) parsing table with the following rules. S -> S + S + S (rule 1) S -> S + S (rule 2) S -> y Is reducing rule 2, then shifting + and y, then again rule 2, equivalent ...
3
votes
1answer
75 views

How to convert a grammar with finitely many ambiguous strings into a new, unambiguous grammar?

Suppose $L$ is an infinite CFL, and $G$ is a grammar with finitely many ambiguous strings which generates $L$. Is it possible to convert $G$ into an unambiguous grammar which also generates $L$? If ...
0
votes
1answer
42 views

How does the Earley Parser store possible parses of an ambiguous sentence?

I've got a pretty basic question concerning the Earley parser: In case of syntactic ambiguity ( S -> NP VP(V NP(NP PP)) vs. S -> NP VP(VP((V NP) PP) ), are both parses stored in one chart or in two? ...
4
votes
1answer
111 views

Show that every grammar for an inherently ambiguous CFL has infinitely many ambiguities

Prove that if a CFL $L$ is inherently ambiguous, then for any grammar $G$ with $L(G) = L$, there are infinitely many strings in $L$ that have (at least) 2 different derivations in $G$. Here's a ...
1
vote
1answer
62 views

Resolving ambiguity in dangling else

Initially the ambiguous grammar is as follows (with some cropped production rules): ...
-1
votes
2answers
41 views

Ambiguous Grammar to Unambiguous Grammar

I'm wondering if somebody can please help me to understand how I go about converting this grammar to an unambiguous grammar. If you can point me in the right direction, I would greatly appreciate it. ...
0
votes
0answers
20 views

Ambiguous grammar and parser LL(1) conflict

I am having some problems to solve this problem. I have to rewrite the following grammar to make it works with an LL(1) parser $$\begin{align*} S &\to  \text{noun} \mid \text{noun and noun} ...
1
vote
1answer
98 views

Unambiguous CFG for $a^ib^j$ where $i \le j \le 2i$

could you please help me for finding an unambiguous CFG for the following expression: $a^ib^j$ where $i \le j \le 2i$
-3
votes
1answer
40 views

Find an unambiguous grammar [closed]

S → aS | aSbS | (empty) where the alphabet is {a,b} in other words, the set of strings where any prefix has at least as many 'a's as 'b's.
2
votes
2answers
57 views

Lexing and parsing a language with juxtaposition as an operator

Normal human math notation treats juxtaposition as implied multiplication, e.g., $2x$ means $2$ multiplied by $x$. This does not seem to be a common feature of computer languages, although it was, for ...
-5
votes
1answer
40 views

Show that this grammar is ambiguous [closed]

$E\rightarrow E+E | E*E | \neg E | (E) | num$ prove the above grammar is ambiguous by giving 2 different parse trees for the expression 4*(~3+5)
5
votes
1answer
92 views

How do I reconstruct the forest of syntax trees from the Earley vector?

Using the Earley vector as a recognizer is quite straightforward: when the end of the string is reached, you just have to check for a completed axiomatic production started at position 0. If you have ...
5
votes
2answers
483 views

does every CFL have an ambiguous CFG?

some questions have been popping up recently on ambiguity in CFLs/CFGs which can have subtleties (eg languages vs grammars & ambiguity vs inherent ambiguity). wikipedia states: Many [context ...
2
votes
1answer
68 views

parsing at semantic level due to ambiguities

I have a VHDL elaboration engine/simulator. As I understand it, the language syntax allows for ambiguities at syntax level. That is, an assignment ...
0
votes
0answers
18 views

Unambiguous Context free Grammar [duplicate]

I was reading through Context Free Grammar, and I came across ambiguous grammar. If the language produced by CFG has more then 1 parse tree, then CFG is an ambiguous grammar. Is there any way by which ...
3
votes
2answers
554 views

Proof that there is unambigous grammar for every regular language

How can I prove, or where can I find proof that for every regular language there is unambigous grammar?
0
votes
1answer
151 views

Determine if two grammars for the same language are ambiguous

I'm reading the book: Formal Syntax and Semantics of Programming Languages. I don't understand this exercise: Consider the following two grammars, each of which generates strings of correctly ...
4
votes
2answers
105 views

Priority in formal grammar

From my recitation class, I have the following exercise: $\mathrm{EXP} = 0 \mid 1 \mid b \mathrm{EXP} \mid \mathrm{EXP} a \mid \mathrm{EXP} m \mathrm{EXP}$ The above grammar is ambiguous. ...
2
votes
1answer
284 views

Is the ambiguity of a regular tree grammar decidable?

Is there an algorithm which decides whether a regular tree grammar $G$ is ambiguous, i.g. there exists a tree $t\in L(G)$ which can be parsed by the grammar in more than one ways, using only leftmost ...
1
vote
2answers
203 views

Is there a name/interest for regular languages that have a non-ambiguous ending?

The basic idea is to have one or more symbol that clearly indicate the end. For example: Non-ambiguous: $ab^*c$ $(a|b)c$ $ab^+c$ $ab?c$ $a(b|c)$ $c(ab)^*ccc$ $acc^*d$ ...
2
votes
2answers
1k views

How to show that given language is unambiguous

Given following grammar: $$ \begin{align} S \rightarrow &A1B \\ A \rightarrow & 0A \mid \varepsilon \\ B \rightarrow & 0B \mid 1B \mid \varepsilon \\ \end{align} $$ How can I show that ...
1
vote
2answers
693 views

In general, how does one make a context-free grammar unambiguous?

Say I have a context-free grammar defined by the following rule. $$ \langle EXPR\rangle \rightarrow \langle EXPR\rangle + \langle EXPR\rangle~|~\langle EXPR\rangle \times \langle ...
4
votes
2answers
732 views

Inherent ambiguity of the language $L_2 = \{a^nb^mc^m \;|\; m,n \geq 1\}\cup \{a^nb^nc^m \;|\; m,n \geq 1\}$

I went through a question asking me to choose the inherently ambiguous language among a set of options. $$L_1 = \{a^nb^mc^md^n \;|\; m,n \geq 1\}\cup \{a^nb^nc^md^m \;|\; m,n \geq 1\}$$ $$and$$ $$L_2 ...
4
votes
1answer
132 views

Hardness of ambiguity/non-ambiguity for context-free grammars

A grammar is ambiguous if at least one of the words in the language it defines can be parsed in more than one way. A simple example of an ambiguous grammar $$ E \rightarrow E+E \ |\ E*E \ |\ 0 \ |\ ...
4
votes
1answer
176 views

What precisely is infinite ambiguity in a grammar?

From what I've read, an example of infinite ambiguity is usually given in a form of a loop: $S \rightarrow aA \\ A \rightarrow B \\ B \rightarrow A \\ B \rightarrow b$ But a grammar is called ...
5
votes
0answers
148 views

How to disambiguate symbolic regular expressions

What I mean by a "symbolic regular expression" (if there already is a different name for this I'm not aware of it) is a regular expression that may include exponents that are symbolic arithmetic ...
4
votes
3answers
5k views

How to prove that a grammar is unambiguous?

My problem is how can I prove that a grammar is unambiguous? I have the following grammar: $$S → statement ∣ \mbox{if } expression \mbox{ then } S ∣ \mbox{if } expression \mbox{ then } S \mbox{ else } ...
0
votes
1answer
305 views

Is this grammar ambiguous?

I have the grammar: $\qquad \begin{align} S &\to S = P \mid S \neq P \mid P \\ P &\to NUM \end{align}$ This grammar suffers from left recursion. To eliminate left recursion, I got: ...