context-free-grammar

I have this grammar S->S+S|SS|(S)|S*|a I want to know how to eliminate the left recursion from this grammar because the S+S is really confusing... Let's see if we can simplify the given grammar. S -> S*|S+S|SS|(S)|a We can write it as; S -> S*|SQ|SS|B|a Q -> +S B -> (S) Now, you can eliminate left recursion in familiar territory. S -> BS'|aS' S' -> *S'|QS'|SS'|e Q -> +S B -> (S) Note that e is epsilon/lambda. We have removed the left recursion, so we no longer have need of Q and B. S -> (S)S'|aS' S' -> *S'|+SS'|SS'|e You'll find this useful when dealing with left recursion elimination . My

L = {1 i - 1 j = 1 i-j : i-j >= 0, i,j>=0} I'm confused about how to construct a grammar that tracks subtraction of a string element. I have no clue on how to get started on this and attempted to work with an equivaent construction of the form L = {1 i = 1 i-j + 1 j } Any hints or suggrstions are appreciated. Here's a tip: always try to think of context-free languages in terms of parenthetic balancing. Consider the following two languages: ab () aabb (()) aaabbb ((())) aaaabbbb (((()))) ... ... Most of us "see" the first language as a repetition (some a's followed by the same number of b's)

I have the following problem: Languages L1 = {a^n * b^n : n>=0} and L2 = {b^n * a^n : n>=0} are context free languages so they are closed under the L1L2 so L={a^n * b^2n A^n : n>=0} must be context free too because it is generated by a closure property. I have to prove if this is true or not. So I checked the L language and I don’t think that it is context free then I also saw that L2 is just L1 reversed. Do I have to check if L1, L2 are deterministic? L1={a n b n : n>=0} and L2={b n a n : n>=0} are both context free. Since context-free languages are closed under concatenation, L3=L1L2 is also

I have been looking for this, but there is a lot of different answers to this question on the MSDN forums . Some people say that "All computer language grammars are context free" and others say that any language that has white-space sensitive syntax is likely context-sensitive and therefore not context-free (F# and Python). Whould be nice a definitive answer and maybe some proof. Mike Zboray I would describe C# as having a context-free grammar, but the language has context-sensitive rules that are not expressed in the grammar. From Wikipedia ( Formal grammar ): A context-free grammar is a

I'm trying to combine both the result of a semantic and a dictation request in the semantic value of a SRGS document. For example, I would say "Search potato" and the output would be something like out="Search Potato" where Potato is a random word spoken by the user. I tought about using the garbage special rule, but it doesn't seem to work. So far that's what I have : <rule id="rule1" scope="public"> <one-of> <item xml:lang="en-us">Search</item> <item>Cherche</item> </one-of> <tag>out.command="Search"</tag> <tag>out.param1=<ruleref special="GARBAGE"/></tag> <tag>out=out.command+out.param1;<

So I've been trying to write a calculator with Scala's parser, and it's been fun, except that I found that operator associativity is backwards, and that when I try to make my grammar left-recursive, even though it's completely unambiguous, I get a stack overflow. To clarify, if I have a rule like: def subtract: Parser[Int] = num ~ "-" ~ add { x => x._1._1 - x._2 } then evaluating 7 - 4 - 3 comes out to be 6 instead of 0. The way I have actually implemented this is that I am composing a binary tree where operators are non-leaf nodes, and leaf nodes are numbers. The way I evaluate the tree is

Are there any tools to convert ANTLR grammar syntax to and from other BNF syntaxes? There are several forms Backus-Naur Form (BNF, EBNF, ABNF, W3C-BNF, XBNF...) with specification, e.g. see this list . The ANTLR grammar syntax only seems to be described by examples . I know that ANTLR grammar files contain more than the specification of a context-free syntax, but you should be able to convert at least the common subset - has anyone done yet automatically? Jakob wrote: The ANTLR grammar syntax only seems to be described by examples. ANTLR (v3) is written "in its own words" (as Terence Parr