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0answers
15 views

Do automatons and formal grammars belong to formal systems

A formal system consists of a formal language, a formal grammar that generates the language, a set of axioms, and a set of inference rules. Are automatons also formal systems? Is an automaton ...
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1answer
32 views

What are the differences between a collation and a rule of formation?

I'm a beginner in mathematical logic, and currently studying(myself, without any colleague, which is sad and so asking in here) basics of formal system. Before asking a question, I'll introduce my ...
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2answers
143 views

$\beta$ - conversion and $\alpha$-reduction problem in $\lambda$-calculus

Here is an expression that I am trying to reduce and my operations so far: $$((\lambda x.(x (\lambda z.zy))) (\lambda z.\lambda y. zy) )= (x (\lambda z.zy))[x \to \lambda z.\lambda y. zy ] = ...
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1answer
56 views

Is this $\beta$-reduction well defined?

Would it be possible to apply $(\lambda x.\lambda y. x)$ to the argument $y$? It seems to me that this must not be possible as it would give a different answer if applied to a constant, call it ...
2
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3answers
255 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
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2answers
317 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 ...
3
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2answers
604 views

Determining if a grammar can be converted to LL(1)/LL(k)

(This is a cross-post of http://cstheory.stackexchange.com/questions/11676/determining-if-a-grammar-can-be-converted-to-ll1-llk in the hopes of gaining a wider audience.) I'd like to know if there is ...
1
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1answer
269 views

Differences between the formal grammar, formation rules and automaton for a formal language

Added: A formal grammar is a set of formation rules for strings in a formal language. Formation rules are rules for describing which strings of symbols formed from the alphabet of a formal language ...
3
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1answer
123 views

Axiom and concept

Is there a concept called "concept" defined in a formal system? Can concepts always be treated as axioms? Can axioms always be used to define concepts? For example, in ZFC set theory, I think the ...