How can we determine whether a given context-free grammar generates any strings at all? Is this problem decidable?
Determining whether a given context-free grammar generates any strings is an important problem in the field of computational complexity theory. This problem falls under the umbrella of decidability, which deals with the question of whether an algorithm can determine a certain property for all inputs. In the case of context-free grammars, the problem of determining
Can we determine whether the complement of a context-free grammar is also context-free? Is this problem decidable?
Determining whether the complement of a context-free grammar is also context-free and whether this problem is decidable falls within the realm of computational complexity theory. In this field, we explore the inherent difficulty of solving computational problems and classify them based on their computational resources required. The decidability of a problem refers to the existence
Is it decidable to determine whether a context-free grammar is ambiguous?
Determining whether a context-free grammar is ambiguous is a problem that falls within the realm of computational complexity theory. In this field, the focus is on understanding the inherent computational difficulty of solving various problems. The decidability of a problem refers to the existence of an algorithm that can correctly determine the answer for all
- Published in Cybersecurity, EITC/IS/CCTF Computational Complexity Theory Fundamentals, Decidability, Problems concerning Context-Free Languages, Examination review
Is it possible to determine whether two context-free grammars accept the same language? Is this problem decidable?
Determining whether two context-free grammars accept the same language is indeed possible. However, the problem of deciding whether two context-free grammars accept the same language, also known as the "Equivalence of Context-Free Grammars" problem, is undecidable. In other words, there is no algorithm that can always determine whether two context-free grammars accept the same language.
Can we determine whether a given string is accepted by a context-free grammar? Is this problem decidable?
Determining whether a given string is accepted by a context-free grammar is a fundamental problem in computational complexity theory. This problem falls under the broader category of decidability, which deals with determining whether a particular property holds for a given input. In the case of context-free grammars, the problem of string acceptance is indeed decidable.
- Published in Cybersecurity, EITC/IS/CCTF Computational Complexity Theory Fundamentals, Decidability, Problems concerning Context-Free Languages, Examination review