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2
votes
1answer
246 views

Restricted read twice BDDs and context free grammars

Several papers give poly-time algorithms for constrained paths on labelled graphs, e.g. [1] Quote: Given an alphabet Σ, a (directed) graph G whose edges are weighted and Σ-labeled, and a formal ...
4
votes
3answers
335 views

Aftermath of the incompletness theorem proof

This is somewhat of a minor point about the incompletness theorem, but I'm always a little unsure: So one proves that there is a formula which is unprovable in the theory of consideration. Okay, at ...
9
votes
5answers
1k views

Resources for learning formal math?

I'd like to learn formal math. Preferably, though not necessarily, starting with predicate logic/first order logic rather than higher order logic. I am trying to find resources (papers, books etc.) ...
5
votes
5answers
685 views

Can a polynomial size CFG over large alphabet describe a language, where each terminal appears even number of times?

Can a CFG over large alphabet describe a language, where each terminal appears even number of times? If yes, would the Chomsky Normal Form be polynomial in |Σ| ? EDIT: What about a language where ...
2
votes
3answers
252 views

Why can't we use memoization to parse unambiguous context-free grammars in linear time?

This is a follow-up question to Why is it hard to parse unambiguous context-free grammar in linear time? I know that Parsing Expression Grammars (PEG) can be parsed in linear time using a packrat ...
1
vote
2answers
315 views

Why is it hard to parse unambiguous context-free grammar in linear time?

From this question, I gather that whether unambiguous CF grammar can be parsed in linear time is an open problem. I'd like to know what the major roadblocks to achieve this are. That is, what made the ...
4
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2answers
3k views

What makes a context free grammar ambiguous?

What makes a context free grammar ambiguous?
0
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3answers
79 views

Are axioms assumed to be true in a formal system?

In a logical system, there is assignment of truth values to the sentences in the language, and axioms are assigned the true value. A logical system is a formal system. In a formal system, there is ...