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Is there anything in the literature about $2k$-nary infix grammars, in particular easy validity and parsing schemes?

$L=langle G_1,G_2 rangle in R$?

0

$begingroup$

Suppose $k$ is a positive integer: I'm working with the $2k$-nary infix grammar
$$
S to mathrmopd | SSldots S mathrmopr SSldots S,
$$
where there are $k$ $S$s in each side of the $mathrmopr$.

This is a CFG, so the rich theory of CFG's and PDA's applies, and it's also obvious that the grammar is ambiguous as is (without parentheses or precedence rules). But far more simplistically --

I have found a very easy algorithm involving just counting how many $mathrmopd$s are in between pairs of $mathrmopr$s to validate expressions in the language and which provides a parse for valid expressions.

Is this result new and/or interesting?

context-free-grammar

share|cite|improve this question

edited Mar 20 at 20:02

Daniele Tampieri

2,62221022

asked Mar 20 at 18:20

Steven MinskerSteven Minsker

11

$endgroup$

add a comment | 

0

$begingroup$

Suppose $k$ is a positive integer: I'm working with the $2k$-nary infix grammar
$$
S to mathrmopd | SSldots S mathrmopr SSldots S,
$$
where there are $k$ $S$s in each side of the $mathrmopr$.

This is a CFG, so the rich theory of CFG's and PDA's applies, and it's also obvious that the grammar is ambiguous as is (without parentheses or precedence rules). But far more simplistically --

I have found a very easy algorithm involving just counting how many $mathrmopd$s are in between pairs of $mathrmopr$s to validate expressions in the language and which provides a parse for valid expressions.

Is this result new and/or interesting?

context-free-grammar

share|cite|improve this question

edited Mar 20 at 20:02

Daniele Tampieri

2,62221022

asked Mar 20 at 18:20

Steven MinskerSteven Minsker

11

$endgroup$

add a comment | 

$begingroup$

Suppose $k$ is a positive integer: I'm working with the $2k$-nary infix grammar
$$
S to mathrmopd | SSldots S mathrmopr SSldots S,
$$
where there are $k$ $S$s in each side of the $mathrmopr$.

This is a CFG, so the rich theory of CFG's and PDA's applies, and it's also obvious that the grammar is ambiguous as is (without parentheses or precedence rules). But far more simplistically --

I have found a very easy algorithm involving just counting how many $mathrmopd$s are in between pairs of $mathrmopr$s to validate expressions in the language and which provides a parse for valid expressions.

Is this result new and/or interesting?

context-free-grammar

share|cite|improve this question

edited Mar 20 at 20:02

Daniele Tampieri

2,62221022

asked Mar 20 at 18:20

Steven MinskerSteven Minsker

11

$endgroup$

share|cite|improve this question

edited Mar 20 at 20:02

Daniele Tampieri

2,62221022

asked Mar 20 at 18:20

Steven MinskerSteven Minsker

11

share|cite|improve this question

edited Mar 20 at 20:02

Daniele Tampieri

2,62221022

asked Mar 20 at 18:20

Steven MinskerSteven Minsker

11

edited Mar 20 at 20:02

Daniele Tampieri

2,62221022

edited Mar 20 at 20:02

Daniele Tampieri

2,62221022

asked Mar 20 at 18:20

Steven MinskerSteven Minsker

11

asked Mar 20 at 18:20

Steven MinskerSteven Minsker

11