What is a regular language?

I’m trying to understand the concept of languages levels (regular, context free, context sensitive, etc.). I can look this up easily, but all explanations I find are a load of symbols and talk about sets. I have two questions: Can you describe in words what a regular language is, and how the languages differ? Where … Read more

Why can’t C++ be parsed with a LR(1) parser?

I was reading about parsers and parser generators and found this statement in wikipedia’s LR parsing -page: Many programming languages can be parsed using some variation of an LR parser. One notable exception is C++. Why is it so? What particular property of C++ causes it to be impossible to parse with LR parsers? Using … Read more

What is the difference between the input set of a BSS RAM and a language?

I’m currently learning some things about BSS RAMs. For sake of simplicity, please imagine them as a Turing machine over the reals. Now, this machine gets some real numbers as input. The input values form nearly a string, but are not of finite length as decimal representation. Additionally, there are infinitely many real numbers. A … Read more

Is the set of context free grammars that generate all words in co-RE?

Is {⟨G⟩|L(G)=∑⋆} in co-RE? ⟨G⟩ is the encoding of a context free grammar. My intuition is that this is false. Answer For A={⟨G⟩∣L(G)≠Σ∗} this procedure, returns “yes” iff there is a word w∉L(G) for a given grammar encoding ⟨G⟩ and never halts otherwise: Assume the input encodes a context-free grammar G. Otherwise, accept the input … Read more

Efficiency/Redundancy in Chomsky normal form

I have a context-free grammar with the following production rules, S being the start symbol: S→ABA→aB→a Is this in Chomsky normal form? My problem is I thought CNF is supposed to be an efficient way to write a grammar, yet the grammar is not efficient in the sense that we can clean its rules as … Read more

Why full Chomsky hierarchy is so detailed, if there are decidable recursive languages?

One can have a look on the Chomsky hierarchy https://en.wikipedia.org/wiki/Chomsky_hierarchy , especially the inset named “Automata theory: formal languages and formal grammars” at the bottom of the page. When one tries to model natural language (e.g. as http://www.grammaticalframework.org/ tries to do it), then one usually aims for the most expressive formal language that is still … Read more

How to create model for a powerful language whose programs are guaranteed to terminate?

I’m creating a powerful regular expression matching system that can be augmented by adding small microprograms to deterministic finite automaton (DFA) states. The microprogram solves the big bang issue where a rule of the form .*ab.*cd doubles the state count of the DFA. The solution for the “big bang” problem is to create a program-augmented-DFA … Read more

Pumping Lemma vs Myhill-Nerode [duplicate]

This question already has answers here: How to prove that a language is not regular? (10 answers) Closed 2 years ago. I was searching for a difference on both ways of proving that a language is not regular but I didn’t came up with much. Let us take the following as an example: L={anbn∣n≥0} Could … Read more