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Questions tagged [chomsky-hierarchy]

The Chomsky Hierarchy is the model proposed by Noam Chomsky in 1956 for classes of Formal Grammars. They refer to Type-0, Type-1, Type-2 and Type-3 grammars which refer to Unrestricted Grammars, Content Sensitive Grammars, Context Free Grammars and Regular Grammars.

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Why does the Pumping-lemma for context-free languages use uvwxy, but the one for regular ones uvw?

Basically what the title says. Why can you "ignore" the "xy" part if you want to prove whether a language is regular?
justdeko
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Expressive power of formal systems

How do we classify formal systems' (propositional logic, first-order logic, second-order logic, higher-order logic, Hoare logic and type theory) expressivity? In the same way that grammars (CSG, CFG, ...), languages (CSL, tree-adjoining language,…
Ito Rapenaer
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How did each class of languages receive their name?

If we look at the Chomsky hierarchy, we see that there are four well-known classes of languages: regular languages, context-free languages, context-sensitive languages, and recursively enumerable languages. There's also the class of recursive…
user11597
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Formal Languages Classes

Are there intermediate language classes between regular languages and context-free languages that can be recognized by automata requiring extensions beyond standard DFA/NFA capabilities but without relying on a stack, like in PDAs?
Cal
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Where can we put primitive recursive functions in Chomsky hierarchy?

I am currently studying recursion theory, but I cannot really understand where to put the Primitive Recursive functions in the Chomsky hierarchy. In my understanding, Primitive Recursive functions contain all finite languages but are not contained…
Briomkez
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What is the big-O (worst-case upper bound) for time and space requirement of the different Chomsky classes?

Everybody knows the Chomsky-hierarchy for describing formal languages and big-O notation for describing time and space complexity of a function. We know, that each class in the Chomsky-hierarchy corresponds to an atomata, that can recognize any…
deadbeef
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Why is Dyck-2 so important for the Chomsky-Schützenberger theorem?

I have read a lot of times, that models that can parse Dyck-2 are of great importance. It appears that Dyck-2 is interchangeably used like Dyck-N. Afaik the Chomsky-Schützenberger representation theorem states that you can convert and context-free…
Crea Teeth
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Where is simply typed lambda calculus on the Chomsky hiererchy?

The functions definable in untyped lambda calculus are the computable functions, for which it is in turn possible to define equivalences to the concepts of Turing machines, recursive enumerability and Type-0 grammars. But what about typed lambda…
Natalie Clarius
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How can the intersection of CFLs and REGs be CFL if REG is a proper subset of CFL?

Intersection of CFL and regular is always CFL. But according to Chomsky hierarchy diagram, regular languages lie completely inside CFL. So, as regular set is completely inside CFL set, their intersection should be regular right ? Am I interpreting…
Ramesh
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Do Combinational Logic circuits describe a set of languages?

I was looking at this picture: https://upload.wikimedia.org/wikipedia/commons/thumb/a/a2/Automata_theory.svg/640px-Automata_theory.svg.png Which made me think, that if all Turing Machines PDA's and FSA's recognize certain sets of languages, there…
zython
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What is the computational complexity of "real-life" regular expressions?

Regular expressions in the sense as equivalent to regular (Chomsky type 3) languages know concatenation xy, alternation (x|y), and the Kleenee star x*. "Real-life" regular expressions as used in programming usually have a lot more operations…
Natalie Clarius
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Does type-1 lambda calculus exist?

I'm interested in the intersection of linguistics and computer science, I've been reading on Chomsky hierarchy, and would like to know if there exist lambda calculus types that are equivalent to the Chomsky types, especially the type-1 that's…
nathias
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Chomsky Hierarchy and P vs NP

I have read multiple questions here that involve this kind of subject but I haven't found any definite answer. In what class do regular languages belong? (P or NP or some regular are P and other NP), context-free languages? (same question)…
user102382
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Is the empty string a terminal symbol?

I ask this question with regards to a grammar in Chosmky Normal Form. The definition states that the rules must be of the following forms: A $\rightarrow$ BC A $\rightarrow$ a S $\rightarrow$ $\epsilon$ And A,B and C are non-terminal symbols, B…
SBylemans
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When did "regular" start referring to Type 3 languages/grammars?

In his 1959 paper, On Certain Formal Properties of Grammars, Chomsky defined a "regular" grammar as a specific form of a type 2 (context-free) grammar. (See Definition 8 of that paper.) He then goes on (in Section 6) to demonstrate that regular…
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