Commit b62747670fbea263d35022fb704bc3b876beace4 - Fountain

Write section about "Doesn't a CSG do what Fountain does?" Chris Pressey 2 years ago

2 changed file(s) with 24 addition(s) and 3 deletion(s). Raw diff Collapse all Expand all

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README.md less more

59	59	* Isn't Fountain really a programming language in disguise?
60	60	* What complexity class does Fountain aim to capture?
61	61	* Is generating a string that is a member of a CSL also in PSPACE?
62		* How does Fountain ensure no Fountain program strays outside PSPACE?
	62	* How does Fountain ensure no Fountain grammar strays outside PSPACE?
63	63	* What if we restrict Fountain to well-founded recursion?
64	64	* What if we forbid recursion entirely?
65	65

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doc/Fountain-Design-Questions.md less more

24	24
25	25	### Doesn't a Context-Sensitive Grammar (CSG) do what Fountain does?
26	26
27		TBW
	27	It's true that every CSL can be described with a CSG -- in fact,
	28	the CSLs are defined as the languages accepted by CSGs. However, the
	29	way that a CSG operates is very different from how Fountain operates.
	30
	31	By CSG I'm referring to "Type-2" in the Chomsky hierarchy. The grammars
	32	in the Chomsky hierarchy are basically string-rewriting systems.
	33
	34	When context is involved in such a rewriting system, that context is
	35	"shuttled around" from production to production during parsing, much
	36	like how the head of a single-tape Turing machine must traverse
	37	potentially large distances of the tape, to access data that is
	38	relevant to what it's doing at some other location on the tape.
	39
	40	For a theoretical construct this is fine. For a practical parser
	41	(or generator) though, all this shuttling makes it a really poor way
	42	to parse (or generate) strings of a language.
	43
	44	Fountain, on the other hand, much like Attribute Grammars (AGs),
	45	stores its context in an ancillary structure which is essentially
	46	random-access and independent of the linear storage of the terminals
	47	or nonterminals of the string being parsed or generated. This makes
	48	it a much more efficient choice for dealing with context-sensitivity.
28	49
29	50	### Isn't Fountain really a programming language in disguise?
30	51

87	108	Then we'd need to weaken our complexity claim to something like "When generating
88	109	a string terminates, it uses only polynomial space".
89	110
90		### How does Fountain ensure no Fountain program strays outside PSPACE?
	111	### How does Fountain ensure no Fountain grammar strays outside PSPACE?
91	112
92	113	Preventing Fountain from expressing languages which are not
93	114	context-sensitive is still an open line of inquiry. Clearly we